I live in Brazil and it's very hot here.
In my experience:
Geforce 6xxx all have ball problems, but will work for a few years before showing the problem, except for the 6800 (there were 6800 that failed after 3 months of use, and that failure was on the die, I have one). Gf6200 desktop especially XFX fails after some years (2 or 3), with each reflow it would work for less time.
Geforce on HP Pavilion (especially 6100 and 8400) are total shit, lasted exactly the 1 year warranty. Here in Brazil there was a big collective lawsuit against HP, which forced them to make a recall (but they just changed the motherboards for others with the same shit defect, even today it is possible to find these defective notebooks for sale , nobody wants them)
8xxx desktop series (especially 8600GT) I saw a lot of people baking, and reflowing, but in my experience, I solved most of the problems I encountered just by changing capacitors, same for PS3 fat (nec tokin). The only ps3's I got that really needed reballing and/or chip swapping were launch editions, which usually had a playstation 2 processor on the motherboard. On the other hand, the xbox360 used an ATI chip, and in the vast majority reballing was not viable (the processor could also have soldering problems), I only saw a small improvement in the Jasper board, but still, in the last slim E models, there are some cases of problems with broken spheres.
8xxx series on laptops was a disaster for me. My first one was a 2007 macbook pro I think. It was a core2duo and 8600GT, I played bioshock 1 on it for a few days until it cooked everything. Apple is the most disgraceful manufacturer there is. They purposely make systems with terrible cooling (I believe due to planned obsolescence), I LITERALLY fried an egg on a G4 1.67Ghz powerbook. So I took it apart, polished the heatsink, and drilled two circular holes for the fans to get air in, closed the hole with that thing you put on windows and doors to keep bugs out, put on some decent thermal paste, and voyala! 15 to 20 degrees less on a PPC laptop.
I have an acer 8930G that uses a 9600M GT ddr3 MXM, it is already the 3rd video card that is installed in it. Previously twice had 9600M GT 1024 ddr2 which failed.
ATI 9xxx and X### on laptops: ALL without exception gave me problems. Until today I'm waiting for a chipset to appear on aliexpress for me to fix an Asus that I have great respect for, which has a radeon 9700. By the way, now I remembered, I only had a laptop with ATI 9xxx that I didn't have problems with (but it got very hot) , it was a Dell Inspiron XPS (1st gen) that had a Radeon 9800, and a P4EE, but I didn't keep it very long, the fan noise irritated me, I ended up selling it.
Even the Nintendo Wii had graphics issues with ATI (at least the ones I had)
On nvidia's fault: It's not entirely nvidia's fault. The engineers did a lot of things wrong in the SIM project, but a good part of the blame lies with the Chinese semiconductor manufacturer (I don't remember the name), at the same time, this manufacturer also made ATI chips, and ATI chips also failed. But the beginning of the avalanche started in 2003 with stupid environmental laws, which decided to remove lead from tin used. It took 15 years to perfect the pewter to what we use today which is a bit more robust (but still not strong enough).