apushatayid: No they don’t. I agree with you on this point 100%.
The problem is they still may come in to shop (for their wife and daughters.) And unless the merchant stops that, the issue is unavoidable.
So there are 2 choices essentially. The shop owner can put a sign on the door “Women Only” (sounds more digestable than “No Men Allowed”) and enforce that policy. This would be the preferred alternative, as you seem to agree. The alternative is to have no Kol Isha.