“Big” transactions are transactions which take up a lot of block space. That has no relation to the amount of value you are sending. You can send 100 Bitcoin for the same price that you can send 100 sats. It’s all about blockspace.

I’m not sure why you are assuming that miners will centralize without a block subsidy. Energy and computing are both naturally distributed all around the world, and if one big miner tries to artificially raise fees (which is not even very feasible) then it becomes more profitable for other miners to come back online and mine themselves. It’s a bit of a decentralization feedback loop.