If you mean using PoW to submit transactions directly: Whatever PoW algorithm you use, an attacker can set himself up to solve it optimally. Legitimate users are stuck with mobile phones, smart credit cards, or Javascript in browsers with limited PoW capability. An attacker can create as much proof of work as he wants without depleting any finite resource. So you're trying to ration based on something that is available to an attacker in literally infinite supply. Then what do you do? Replace your computer with a faster one?

If you mean using PoW to distribute a currency: Sure, that works. But it's arbitrary, unfair, and wasteful. It makes perfect sense for bitcoin because it's needed to secure the blockchain. It's functionally equivalent to auctioning off the currency as the people willing to invest the most in obtaining it wind up with it, except the money is wasted instead of put to anything remotely resembling good use.