Out of Pod Experience

Just a few side-notes... not contradicting you, just providing an anecdotal clarificative counterpoint.

I have a couple of old machines semi-gathering dust that still work just fine after a very long number of years.
That includes a Pentium 3 "home server" which had been operational nearly 24/7 for nearly 10 years (only off during house moves, vacations away from home, and obviously during power outages) - no failures so far, but no point using it anymore since the tiny wireless router does almost everything it used to do, it's so much smaller, and uses so much less electricity.
I do not remembering ever having problems with a CPU due to old age other than the obvious "too slow, need faster one" thing, neither for me nor my family. It's possible my brother might have had one CPU eventually going defective once, but I'm not sure about it.
Also, as far as thermal issues go, the only relevant thing is CPU temperature, so if that one's ok-ish (and you can monitor that, I personally use RealTemp, but there's plenty better ones too), the paste might as well be half past gone yet it doesn't really matter if the temp does not go critical - until now I've had a lot more issues with heavy-duty dust and other gunk on the heatsinks and fans rather than old, decrepit thermal paste.

Bull. I call argumentative fallacy here: False attribution – an appeal to the irrelevant.
Also: Red herring.