I think what you're describing is basically a smart contract.
How you design a smart contract is not limited by anything other than your technical ability, then by your own imagination. You could design a smart contract where any transaction that occurs incurs a small transaction fee and the fee is stored in a designated address or "treasury" address where the UTXO can only be spent by having a vote by holders of the token.
The voting functionality would need an off-chain validator function confirming the person voting indeed has some of the correct native asset, and how much they have. Next you would create functions to submit proposals, which again check that the person submitting a proposal holds that specific native token.
So essentially the smart contract would handle the logic of submitting, voting on, and determining which proposal wins and becomes the future of the dApp/protocol/whatever.
This is what makes blockchain so exciting, it's simply up to your imagination. Look into the Uniswap smart contract for a more in-depth look into creating a smart contract with the functionality you defined.