You are right, and it's arguably harder for those smaller boxes sitting in cabinets / on telegraph poles, despite being much lower power systems to start with. It might be 50C+ in there before they even turn on! Those things might have a two-stage boot process where they just run their fans for a bit to cool things down before actually booting the main system. It must be a real nightmare for entirely passive stuff, I have no experience with that.
I was trying to point out that high-end hardware should survive a couple of days despite a data centre losing its cooling. it is designed for exactly that situation.
Sounds like the downside of the "pets versus cattle" methodology is that natural phenomenon will wipe out your entire herd, while the pets survive.