[@Theodorable]System appears to be light enough on the game mechanics to not worry about such.
So long you also avoid stat numbers and players influencing these it's actually easy to keep things pure.
As for overall the system sounds similar to what Alternate History forums and Sufficient Velocity uses, maybe a bit simpler thus more free.
Albeit the idea of saving up leftover action does worry me a bit. It might allow some cheesy things by giving the player freedom to stack up their actions while watching what everyone else does while negating the chance the other side would do the same. I'd say you could invent a theoretical limit to this while also watching out for players who appear to be intentionally making this sorts of play. This is the only potential pitafall I can see. Intentionally saving up a few points is fine, just don't stack up ridiculous numbers. Because I feel it'd be trouble. Kinda the same as having dimension door in Heroes of Might and Magic, especially the earlier games. You stack up sufficient "mana" that you can basically perform several if not dozens of turns worth of stuff without the other side being able to do much to counter it.
While I say this is trouble, all it really requires is you to say "no" when somebody tries to scum like this.

As for tyranny of majority, I don't think it was a trouble in narrative NRPs. The main reason they fail is because there's nothing to really hold them together. Many games are just too freeform and/or lack GM presence to be kept being engaged. With your more prominent presence and sufficient number of players I bet this could be fairly successful.