In a perfect market the profit opportunity asymptotically approaches 0.
But a perfect market is a mathematical model, not something that you would see in real life. As you note some entrant is not going to jump into a market and undercut the competition by 1 cent (from 2 cents) and immediately capture all of the market share.
But this does illustrate the dangers of making a more efficient marketplace if your goal is to make profit.
That doesn't quite right to me. A market with the smallest profit opportunity of a selection (say worse that government bonds) wouldn't see investment to correct that inefficiency. Zero may be 'best' case, practically speaking though no one's going to arbitrage an opportunity, that's less than the opportunity cost.
So it seems to me the optimal market would a profit opportunity somewhere between being the 2nd best profit opportunity and zero profit opportunity, depending what you set the opportunity cost at.