As I say, part worns may have a place for those more concerned with legality than anything else, when new tyres are needed unxpectedly. I still maintain its not a cost effective approach to constantly use part worns - I believe you are paying well over the odds during the course of the life of a NEW set of tyres.
Budget v Premium is a seperate debate altogether. Must budget are awful, but then some premium - Michelin for example - are awful as well.
As to why part worns are available, most people will drive done to near the legal limit, so those that are replaced beforehand are with pulled off writeoffs, occasional puncture, so both sides replaced, or because the original owner realises that by 5mm, they are well past their sell-by date. Very few fleets would remove 5mm+ tyres to sell a car on. Very few.
Tyres can be lethal. That Autogrip one in my garage is a prime example. About 7mm tread, even wear, but poor grip in the dry, but zero, and I mean zero, grip in the wet. I would challenge even the gayest of gays, ie tunnie, to drive that without loosing it.