If consumers paid out of pocket for their phones then they would be more picky about upgrading and plan prices. It would also make upselling shitty plan features harder so the carriers would loose a lot of money.
It wasn't cheaper than all alternatives. There were a bunch of virtual operators offering better monthly rates than the big networks but I've personally had bad experiences with network deprioritization on them. Depends very much on your individual circumstance, I'm in NYC and the network is clearly pretty saturated.
This is generally strictly true, but most people don't move on to the next deal once they've paid off their device, and end up paying more than they would have had they bought the device outright, device+plan cost considered.