Then maybe that these daily quests are only available as soon as they have access.
That would require making the quest system way more complicated than it currently is. Its function seems super simple: it picks a random quest from the pool, disregarding potential other quests the player currently has (because it's possible to get the same quest multiple days in a row), and adds it to the player. Rerolling simply repeats that process.
If a quest were to be conditional, that would require changes in the form of additional coding. Even just a single
if function would add complexity and potentially cause unforeseeable issues in the form of bugs.
There is also the question of
how a player would be deemed "eligible" for SY quests. I can see two main options: a flat "when level X is reached", and something collection-based (e.g. "when a Syndicate deck is acquired"). Obviously the latter would be the much better option of the two.
But all things considered, I'd say it's fine the way it is. You can use Syndicate for all but the faction-specific quests, and I don't see any sense in such a change for the sake of maybe marginally increasing the faction's playrate.
Syndicate has never been equal to the other factions, because it was never intended to in terms of accessibility and difficulty of piloting (the devs said that sometime in 2019, prior to the Novigrad expansion).
