> It's impossible to convince the "frequent upgrader" that maybe that's a risk in terms of introducing new issues

I would count myself as a "frequent upgrader" - I admin a bunch of Ubuntu machines and typically set them to auto-update each night. However, I am aware of the risks of introducing new issues, but that's offset by the risks of not upgrading when new bugs are found and patched. There's also the issue of organisations that fall far behind on versions of software which then creates an even bigger problem, though this is more common with Windows/proprietary software as you have less control over that. At least with Linux, you can generally find ways to install e.g. old versions of Java that may be required for specific tools.

There's no simple one-size-fits-all and it depends on the organisation's pool of skills as to whether it's better to proactively upgrade or to reluctantly upgrade at a slower pace. In my experience, the bugs introduced by new versions of software are easier to fix/workaround than the various issues of old software versions.