The logic to assign mulligan charges to leader should be based on how the leader as a single entity can turn the tide of the war. So,
1 Charge : The Leader has a very strong innate abilities and powers which can potentially win the entire game based on an archetype. The leader synergies with a lot of cards. So, with 1 mulligan charges, it would be hard to use cards like Roach and even harder to use WitcherTrio
2 Charges: The Leader has a strong ability with which a single round can be won easily. Cards like Roach or WitcherTrio should be a little riskier, but they can pull it off if planning carefully.
3 Charges: The Leader is strong. Even though a round can not be won just with his/her abilities, it can greatly help with appropriate hand. Three mulligans is necessary for them to pull their 'trump card (and the assisting cards)' to win a round.
4 Charges: The Leader is weak. Just with his ability alone he/she can't win a single round. He/She would need elaborate setup required to win a round and the game. So, four mulligan charges are absolute necessary.
0 Charges: The Leader is rather devastating such that he/she doesn't deserve any charges.
So, with this rough definition: Lets go through the leaders and see how many mulligan charges they should have:
ST:
Franchesca: NO Change. She can win a round with her ability easily with good deck building.
DwarfKing: With just 3 usages and an impact of 6 point swing, he will need good amount of mulligans to get a good deck. He can be strong with weather and counters units that are row locked. 3 seems OK, but may be 4 will make him too strong? I am fine with 3 or 4.
Filandravel: He can't win a single round just with his ability. Due to his ability, he may need to avoid special cards which is kind of weakening him? 4 is apt for him
Eithnè: She is strong. Even if artifacts are nerfed, with so many SC units which can do damage in many flexible way, she can align the units for Epidemi or Scorch or Regis. I was thinking once artifacts are nerfed, she will become weak, but after careful thinking, she seems to be strongest SC leader: 1 or 2 mulligans only for her.
SK: [I have never played a single SK game, so I may be wrong here. Expert SK players can pitch in.]
Eist: His current ability is underwhelming. Is there any really powerful warrior who returns to the war and win a round? But nonetheless, it is like playing 2 units in a round and may win you the round. 3 seems a little less. 4 is OK (but if new powerful warriors are added, then it should be moved to 2 mulligan charges).
Harald: He can do 8 damage and can work well with GS or blood third archetype and his ability can win a round easily. If he goes last, it is a guaranteed win. Because his last play can swing 19 points. 2 mulligan charges.
Crach an Craite: He is a weak flavor of Eithnè. He can greatly support blood thirst archetype. He can align for G:I or Epidemic or Scorch (even if not as efficient as Eithnè). He should have 3. He is not very weak to give 4 charges.
Bran: Ideally he doesn't care about mulligan at all. He can thin the deck to 0. So, even if he get 0, it is OK.
NG:
Usurper: Perfect 0
Calveit: With playing 2 cards in a turn round, can give him significant advantages and can get him a round win. 2 Charges.
Emhyr: Playing a gold card twice is an incredible ability. It can easily win a round. 2 Charges.
Voorhis: He can get +3 or +4 boost per round. It is not overwhelming. The reveal cards are over powered and can be used by any leader, but Voorhis's ability is not a game or round changer. 4 Charges.
MO:
Eredin: With an immune Gaeles or Sabbath or Ciri he can gain significant advantage and win a round easily. Immediate Immune is super cool. He should have 2 charges.
AQ: Very strong with consume archetype and can easily overpower and win an entire game with the right cards in hand. 1 Charge.
UE: Trigerring the DW of a unit is a good power. A decent DW can get +5 points. +5 points per round is a very good boost. But doesn't mean it is like an insta round win. 3 Charges.
WS: +8 can usually win a round. 2 Charges
NR:
Foltest: With 3 order abilities available immediately, he can disrupt any strategy and kill 3 important units without any way to stop it. With more mulligan charges he can always get the strongest Golds and W3Trio and can potentially win a game. He should have 1 mulligan charges if he is to retain his current ability.
Demavand: Is very strong and can have effect throughout the game, but at least gives the chances to lock the units. 2 Charges.
Henslet: I am not sure if there is any combo he can pull it off for winning a round. He can max play a bronze card? I don't know how people use it since I haven't faced him till now. So, in the current form I think he is the weakest NR leader? 4 Charges
Adda: +8 points is good enough that it can win a round. With no synergy with any other cards, she may have 3 charges.
This is my take. An honest neutral take on leaders and the mulligan charges.
1 Charge : The Leader has a very strong innate abilities and powers which can potentially win the entire game based on an archetype. The leader synergies with a lot of cards. So, with 1 mulligan charges, it would be hard to use cards like Roach and even harder to use WitcherTrio
2 Charges: The Leader has a strong ability with which a single round can be won easily. Cards like Roach or WitcherTrio should be a little riskier, but they can pull it off if planning carefully.
3 Charges: The Leader is strong. Even though a round can not be won just with his/her abilities, it can greatly help with appropriate hand. Three mulligans is necessary for them to pull their 'trump card (and the assisting cards)' to win a round.
4 Charges: The Leader is weak. Just with his ability alone he/she can't win a single round. He/She would need elaborate setup required to win a round and the game. So, four mulligan charges are absolute necessary.
0 Charges: The Leader is rather devastating such that he/she doesn't deserve any charges.
So, with this rough definition: Lets go through the leaders and see how many mulligan charges they should have:
ST:
Franchesca: NO Change. She can win a round with her ability easily with good deck building.
DwarfKing: With just 3 usages and an impact of 6 point swing, he will need good amount of mulligans to get a good deck. He can be strong with weather and counters units that are row locked. 3 seems OK, but may be 4 will make him too strong? I am fine with 3 or 4.
Filandravel: He can't win a single round just with his ability. Due to his ability, he may need to avoid special cards which is kind of weakening him? 4 is apt for him
Eithnè: She is strong. Even if artifacts are nerfed, with so many SC units which can do damage in many flexible way, she can align the units for Epidemi or Scorch or Regis. I was thinking once artifacts are nerfed, she will become weak, but after careful thinking, she seems to be strongest SC leader: 1 or 2 mulligans only for her.
SK: [I have never played a single SK game, so I may be wrong here. Expert SK players can pitch in.]
Eist: His current ability is underwhelming. Is there any really powerful warrior who returns to the war and win a round? But nonetheless, it is like playing 2 units in a round and may win you the round. 3 seems a little less. 4 is OK (but if new powerful warriors are added, then it should be moved to 2 mulligan charges).
Harald: He can do 8 damage and can work well with GS or blood third archetype and his ability can win a round easily. If he goes last, it is a guaranteed win. Because his last play can swing 19 points. 2 mulligan charges.
Crach an Craite: He is a weak flavor of Eithnè. He can greatly support blood thirst archetype. He can align for G:I or Epidemic or Scorch (even if not as efficient as Eithnè). He should have 3. He is not very weak to give 4 charges.
Bran: Ideally he doesn't care about mulligan at all. He can thin the deck to 0. So, even if he get 0, it is OK.
NG:
Usurper: Perfect 0
Calveit: With playing 2 cards in a turn round, can give him significant advantages and can get him a round win. 2 Charges.
Emhyr: Playing a gold card twice is an incredible ability. It can easily win a round. 2 Charges.
Voorhis: He can get +3 or +4 boost per round. It is not overwhelming. The reveal cards are over powered and can be used by any leader, but Voorhis's ability is not a game or round changer. 4 Charges.
MO:
Eredin: With an immune Gaeles or Sabbath or Ciri he can gain significant advantage and win a round easily. Immediate Immune is super cool. He should have 2 charges.
AQ: Very strong with consume archetype and can easily overpower and win an entire game with the right cards in hand. 1 Charge.
UE: Trigerring the DW of a unit is a good power. A decent DW can get +5 points. +5 points per round is a very good boost. But doesn't mean it is like an insta round win. 3 Charges.
WS: +8 can usually win a round. 2 Charges
NR:
Foltest: With 3 order abilities available immediately, he can disrupt any strategy and kill 3 important units without any way to stop it. With more mulligan charges he can always get the strongest Golds and W3Trio and can potentially win a game. He should have 1 mulligan charges if he is to retain his current ability.
Demavand: Is very strong and can have effect throughout the game, but at least gives the chances to lock the units. 2 Charges.
Henslet: I am not sure if there is any combo he can pull it off for winning a round. He can max play a bronze card? I don't know how people use it since I haven't faced him till now. So, in the current form I think he is the weakest NR leader? 4 Charges
Adda: +8 points is good enough that it can win a round. With no synergy with any other cards, she may have 3 charges.
This is my take. An honest neutral take on leaders and the mulligan charges.