Burning a pool for an advantage is a very common mechanic. You can find it everywhere, this idea of spending from a limited pool of resources for a power-up.
For example, in Street Fighter you can use a super move if you spend part of your super bar. In FPS games, weapons with more limited ammo (pools) are more powerful than those with plenty of ammo. In oldschool D&D, your magicians burned spell slots to cast spells.
This mechanic needs to be carefully considered. Normally it is a supporting mechanic rather than a primary one. The reasons are easy to explain: it's the old "quadratic wizards" problem.
See, in D&D a wizard was useless unless he burned up a spell. Low level wizards had a very small pool, so unless the party was going to rest for eight hours every five minutes, the low level wizard was going to spend most of his time useless. However, as the wizard gains levels, he gains spell pool slots, and the whole pool always regenerates at the same speed. Eventually, the regeneration rate matches and then outpaces the burn rate, and you have a quadratic wizard that can burn pool in literally every encounter.
Similarly, an FPS with plenty of ammo, players can spend it like water and not worry about running out.
In a tabletop game, pools usually regenerate very slowly and are prized as resources you absolutely don't want to spend. Hit points are a pool. Health potions in your sack are a pool. Wands of lightning have a limited pool of shots. But if the players get very powerful, these pools become very easy to refill or switch out - someone with eight lightning wands will just go ahead and spam them against everything.
So, the heart of a pool burning mechanic is trying to balance the rate of burn and the rate of regeneration. If you make the pool burning mechanic a core mechanic, you're going to raise the rate of burn exponentially. Can you create a method of regeneration which matches that without regenerating so fast it makes spending pool essentially free?
Let's pretend we have a game where the players have several pools of resources they can burn, and that's their primary mechanic. However, the pool regeneration is slower the more of the pool they have spent.
This is a positive feedback cycle, and is generally an extremely bad call. In a multiplayer game, having the players that do better able to do more better while the players that are struggling have an even harder time... that's generally going to end up with a few gloating munchkins going "man, we have to stop to let you regenerate again?"
On the other hand, you could make it so that the pools regenerate at a specific rate, but if you're low, you can actually go out and refill them using some mechanic that produces role playing. For example, a heroic character might have to help someone to get a rapid pool recharge. A magician might have to uncover secrets that the bearers don't want revealed. You can even make the regeneration system so that the players have to help each other to regenerate pool, which would be fun.
By making the regeneration a core motivation rather than a core limit, you can make the game many times deeper.
Still, at heart, if the game is primarily about choosing how much of which pool to burn, you're going to have a very... fast game. That kind of mechanic isn't very amenable to long confrontations over dozens of turns. Instead, you're likely to have fewer, shorter confrontations. If you want your game to have few confrontations per adventure arc, that's fine.
But if you want to allow more conflicts, you need to either A) radically enhance the pool rules to allow for tons of give and take over the course of a fight or B) come up with another set of core rules to allow the players to act without every action being a worrying choice.
B) is, of course, the path to making your pool burning rules into support rules instead of core rules...
Anyway, that's my thoughts on that.