While throttling itself is a safety feature and not inherently damaging
This is true but that's not always what happens. Thermal throttling is meant to prevent damage and minimize errors.
Thermal throttling is not a feature every CPU has, it's a rather modern thing to find it on PC's and laptops. In fact many CPUs have no way to self-regulate at all. They simply work until they fail. Sometimes that's temporary, as I've experienced many times with routers, and sometimes it's permanent, and sometimes it's a matter of this particular CPU has a lower thermal failure threshold than others.

