There is a Pitfall to be avoided, but we can get to that Now. There have been Tokens made on the Blockchain that made it where, I am not sure on the Math but to make it simple let's say the way it Worked (and this is how it Worked, I am just not sure on the Math) it Released 1 Token Every Time someone did some Specific Action. This seems Fair at First because anyone can come in and get one.
But they found that People could make Several Accounts and be Performing the Action Several Times, and this isn't much Different than ASICs Taking Over Blockchains, but it didn't Work for the Tokenomics. It Quickly became Unfair. Or a 51% Takeover.
51% Takeover used to be a Death Sentence, even if the Token or Coin Maker was the 51% Holder. That is, until Steemit, where they Promised to use the 51%+ that they Held to Fund New Accounts and Community Development. Since then there have been many Projects where the Creators Hold 51%+ and it has been more Accepted than it was before.
But the Point being, Increasing the Rewards Pool to meet Demand does not Work for Mining.
When Mining and doing Proof of Activity, it should be like Proof of Stake. Each Activity should count as like 1 Stake, they are called "Vests" in Steemit Language, and we could use that Word. Each Activity constitutes Vestment, Vests we could say, and the Rewards Pool does not become Larger. Instead, the Coins become more and more Rare.
This is what Bitcoin Mining Calls "Difficulty". As more and more People Mine, the Difficulty goes up, and where You used to be able to Mine with a Laptop, now the Difficulty has gone up, and You need a Mining Farm to do the same Thing a Laptop used to do. Just because there are so many more People with more "Vests", or "Hashrate" in Bitcoin Mining Language. The Vests and Hashrate are Similar.
In Proof of Stake, the Hashrate comes from the Vested/Staked Currency, so they are exactly Correlated. If we just use Proof of Stake as our Standard, then we can make this all Very Simple.
I am making a Proof of Burn Token. So the Burn will be a kind of Vest, or a Share, a Hashrate, once Burned the Hashrate will go to the Wallet that Burned the Token. And the Rewards Pool will not Grow. But instead, that Person gets a Hashrate, and it makes it Harder for Everyone else. The Difficulty goes up.