I've had this exact discussion with friends who study economics. The idea is that in a market with perfect flow of information (i.e. fairy land) then the profits tend to zero, I don't think this is a model for much of the real world if any.
That makes as much sense as people working for nothing. I don't see any explanation for profits tending to zero, either.
I wonder why "perfect" markets are even a thing. It has no applicability to actual markets. It offers no insight on actual markets, and offers no useful predictions about markets. It's about as useful a model as the Monopoly game is - i.e. none.
I've seen many people claim that a "perfect" market is a requirement for free markets to work well. This isn't remotely true. "Perfect" markets and free markets have nothing in common.
"Perfect" markets just seem to be a strawman put forth by people who argue that since "perfect" markets are unachievable, therefore free markets are no good.
"Companies earn just enough profit to stay in business"
which contradicts your comment:
"in a “perfect” market there cannot be profits"