I can think of several reasons why typical markup rates would be relevant, but not for why typical profit margins would be. I suspect you looked up "profit" when what was doing the work in your implicit arguments was "markup".

Profit margins strike me as a better measure of how competitive prices are; markup rates are necessarily higher because of the costs of running the store. To put it another way, high profit margins are a better sign of low competition than high markups.

The argument I was making was that grocery store customers are not a captive market, and are sensitive to price increases (and probably insults).

Also, I think your emphasis on what you see wrong with a 5% toll violates the spirit of least convenient possible world, as I used that as an example of what I thought would approximately achieve the ends I had in mind.

Since I'm pointing out potential downsides of your suggestion, isn't invoking LCPW for me invoking MCPW for yourself?

I am discussing a small improvement to an existing structure.

You are suggesting a small change to an existing structure. It has both positive and negative effects.

I don't really buy the analogy because the point of this is that people could decide what to do after going to the store that has choices and looking at the lines. People like to keep their options open.

The original examples of extra choices making people worse off come from grocery stores (though choice paralysis is different from the game theoretic concerns I'm making).