What can they do? There are very few things they can do that does not have a large impact on the rest of the game.
What can they do? Make changes to reduce the viability of these type of decks. If they impact the rest of the game, so be it. Changes, as in card and mechanic redesigns. Not provision or power adjustments. Yeah, I know, actual work.
Ultimately, every "no unit" deck is based on the following...
1. Non-interactive.
2. Ability to constantly remove opponent positive points.
3. Ability to quickly supply positive points.
To provide an example, Francesca. You could build a Fran deck with a lot of "offensive" spells, buff potions, possibly offensive artifacts, spell tutors, a few boost spells, Saes and something like Renew. 90% of a round is spent removing opponent positive value with non-interactive concepts (offensive spells/artifacts). Incidentally, any opponent "control" is negated, as it has nothing to hit. For the other 5% of the round you could be tossing buff potions at a board to store positive value for later. When the end of a round comes around you dump a big Immune dragon on the board (again, control can't target it). At that point it's a matter of funneling those buffs into it (potions, spells).
Another example? Sihil decks of the past. Essentially, these builds played artifacts, Sihil, ways to return Sihil to the board, (via resurrection to counter AR or play it over multiple rounds), ways to reliably find Sihil and something "big" to take rounds. In games against these decks nearly everything the opponent put down was going to get steamrolled by Sihil. You could spend 80-90% of a round intentionally discarding your cards. In fact, it was often correct to do so to block Sihil from "growing". Those card plays simply did not matter. The important part was when the round was hitting the end point. The Sihil deck then dumps a big play on the board. Witchers come to mind. The opponent then dumps their big card on the board. Since, you know, they kept it because they were smart. Who wins? Who has a bigger unit at this point. That is who wins.
Taking a trip down memory lane.... Spell'tael was a thing in beta. It ran on the same concept. Remove opponent positive points, funnel buffs to hand-buff cards in the process then use those hand-buff cards (#3) to win rounds. Granted, it wasn't nearly to this extreme. You know why? Because, back then, we didn't have artifacts. The only "non-interactive" option available was spells/specials. Insert HC. The developers, in their infinite wisdom, decided we needed more "non-interactive" options (or maybe they just pulled the idea out of a hat... or their asshole... who knows). Now we suddenly have a way to pair and combine two different non-interactive concepts, one of which can store value for later (positive or negative). We also didn't have Immune. Why? Because in CB we had Promote and it was a disaster, so they removed it (and clearly they "learned" from their mistakes... heh heh).
Getting to the point....
1. Remove artifacts from the game completely.
2. Remove Immune from the game completely (replace it with Armor because it's more better).
I'd bet most non-interactive, "no-unit", "special" decks would go poof. The reason being it would become far more difficult to do #1 and #3 all the way at the top of this post in the way these decks do it. Yeah, it would still be doable with a "spell" deck. Such as with Francesca. There wouldn't be 14 ways to do it, however. It would be more in-line with Spell'tael, which even at it's peak was a T2 concept at best, and less like the Sihil builds before the card was nerfed into unplayable land (by the way, good fix team... you fixed it because nobody plays it anymore... sounds fixed to me).
Lastly, people really need to stop pretending there is thinking involved in countering these type of decks. Their approach is extremely simple. The counter-play is incredibly simple. The problem comes when you insert stuff like coin flip and draws. Likewise, it's not about whether these no-unit decks are overpowered, weak, terrible, strong, awesome, etc. They're annoying to play against. Play one three times in a row and, even if you win all three games in convincing fashion, you still feel like playing a different game for a while.