I don't have any solid numbers on me, but I believe early 360s failing wasn't just widespread; it was straight up most of them dying within the first couple years. It's honestly insane they more or less got away with that. And I guess also speaks to how much Microsoft was killing it in that era that people were willing to go through multiple console RMAs (which I heard was a terrible, slow, and unreliable process) to play 360 games. How far they've fallen.
Simple answer: Halo 3.
It was something like 25% - 50% of all first version 360s died.
Microsoft spent over a billion dollars replacing and repairing consoles to maintain the good brand name of Xbox.
https://en.wikipedia.org/wiki/Xbox_360_technical_problems
Family got first gen 360. Still works to this day. We hit the jackpot with that console. It out lasted 2 wiis and a ps2
Whenever we lost a 360 we got a pre owned 360 from gamestop. I think they went for like $70 for one without any hdd.
That was the real story, by the time they started dying you could just grab a working one for "decently cheap" if you still cared.
However, I wonder how many people got "burned" by it and swore off Xbox consoles going forward.
I know that era we got a lot more use out of the Xbox (original) and the Wii.