They should also not be allowed to make secret deals with companies to artificially boost said companies or to downrank non-paying competitors.

The problem is there's no accountability.

Sure, we can sue them, but for what damages? How do you account for the value of lost business opportunities caused by Yelp selling your honestly earned ranking spot on their website to your competitor?

The only way to prove they've done something wrong is to commit corporate espionage and get the proof yourself, which would then most likely invalidate the ability to use that evidence for revenge.