The gas fee is one of the important fees, for the successful exchange of coins both in exchange and wallet address, to my opinion all gas is been shared between miners and liquidity providers and wallet address owners. Traffic when conducting transaction determine the amount of gas fee to pay, when carrying transactions.
Im not sure if those all fees are shared with miners. But I think when someone get your transaction the fees goes to their pool instead. But I think this is how the method on miners since they have their own pool. Cause if all gas fees process by a certain pool also went to others as you mentioned shared then its like it's one profits for all. There are factors on it I guess.