The hype was probably mostly from "Crazy" Ken Kutaragi, who had a knack for dialing the Playstation hype beyond 11. The PS2 was already supposed to replace your home PC and revolutionize ecommerce and online gaming and plug yourself into the Matrix [1]. In the past he was compared to Steve Jobs by some, but in hindsight he seems more like Sony's Baghdad Bob.
I've heard on the grapevine that the PS3's OtherOS facility was internally thought of as another go at the same idea. "Look, judge, it's a general purpose computer for reals this time. Your own universities are using it in super computing clusters, without ever launching a game".
Being forced kicking and screaming into the multicore on the PS3 improved our PC codebase by quite a good margin. So what I'm trying to say is that the hype was real, we have gone multicore, just not with the Cell architecture.
Did the 360 not drag things into multicore very similarly? Pretending its CPU has one core is a pretty similar experience to pretending a PS3 has no SPEs.
[1] https://www.newsweek.com/here-comes-playstation-2-156589