interesting, we need to discuss this more first then :)

the AMM can be easily profitable by simply taking a cut on each trade, then competition will make the amount of this cut just enough so that the operator makes a small profit no?

Even if this AMM is less economically efficient than the same one on Ethereum, nothing will stop users to use it if they want to, knowingly or not that they are not using the most efficient tool.

That's why I say that profit is not an issue per se, only mevil is.

For me this is like saying operating a Lightning node in a profitable way is an issue. It is not, because miners can't extract MEV from LN txs.