I remember Steve Brown saying once that Hironori Mii showed him bind returns back in the late 90s, so they’ve been around at least that long. I don’t think they were that common and were used more for getting tighter winds with low spin than for truly unresponsive play, though. I think the shift generally happened throughout the early- to mid-2000s, starting with players modding their yoyos to be less responsive and gradually moving toward manufacturers catering to unresponsive play. I’m not sure who was the first, but Difeyo had some early unresponsive designs, and YoYoJam had their adjustable gap system that allowed for unresponsive play. Modders would have preceded them, though.
I think 2004 was the first year players were not required to use a responsive yoyo for 1A compulsories (the prelims at Worlds used to be a compulsory trick list instead of freestyles, and for previous years the trick descriptions required the yoyo to be returned without a bind). Players were using unresponsive yoyos in freestyles before that, though there were still a lot players using responsive yoyos in freestyles in the early-2000s.