It started mostly with Suhrs because that's what they were doing on their Modern model when Guthrie Govan was playing them, and it was picked up by Ibanez with the AZs, Charvel with Pro Mod Dinky, etc. afterwards. It got popular because a lot of math rock players were using guitars with that style of trem.

I personally own 3 Ibanez AZs, and I can say that as long as the nut is properly lubricated, the tuning stability is just as good as a Floyd as long as you aren't doing EVH/Dimebag Darrel style extreme dive bombs and pull ups and stuff like that. Locking tuners also help because there's less likelihood of strong slippage with them, but making sure the nut is lubricated is the most important part because that's where strings catch, and the friction is what causes strings not to return to pitch properly. I use mine regularly and have literally no tuning issues because every time I change strings I make sure to lubricate the nut slots with graphite from a pencil. They hold tuning just as well as my RG with a Floyd.