Per other responses, they frequently do charge a special fee (I think Aave charged around 0.09% at one point but can't find good ref right now).

One interesting thing I think is still under dev/consideration is adding the ability for MakerDAO to make "flash mint loans"(https://forum.makerdao.com/t/mip25-flash-mint-module/4400/9) -- essentially a flash loan where the caller can mint an arbitrary amount of DAI without having to back it with anything, so long as they pay it back + fee at the end.

There's a similiar idea being worked out for WETH10 (https://github.com/WETH10/WETH10#flash-loans), a project trying to make a feature update of the WETH (wrapped ether) token.

I'm honestly unsure WTH the impact of something like these would be, but would definitely prevent arbitrage from going too far out of bounds, since there would always be unlimited liquidity.

Multi-party atomic financial transactions are kinda insane.