When you can't imagine or pretend that when a major vuln is disclosed (a) you've been secure up until the point of disclosure or (b) all you need to do now is apply a patch without thinking too much about what your blast radius just was, you might actually have stronger incentives to think about the design of the overall system so that when similar issues come up, you can avoid having to sweat those outages.
It's interesting that "defense-in-depth" gets cited and repeated all the time but the standard attitude about patching still seems to be "what do you mean?? isn't patching the only thing we can do?". How about designing systems so that you can more quickly and easily throw up other kinds of mitigations when you need to? What about designing systems with robust enough notions of graceful degradation that when something crops up for a certain feature you can "just" say "okay, let's turn only that part off for a couple days"? How about getting really, really good at CI/CD so you can more confidently add and deploy mitigations to your application code, or redeploy with a feature flag that lets you temporarily drop an unpatched-and-vulnerable dependency?
If you can manage to build a system without the assumption that just patching is always on the table, you might simply end up with better software, which would be pretty cool.
Care to mention these reasons?
With "convenience of system administrators", I'm guessing you mean that there's a patch available that sysadmins can install, ideally before the vulnerability is disclosed? What else are sysadmins supposed to do, in your opinion? Fix the vulnerability themselves? Or simply shutdown the servers?
With the various copyfails of recent, it at least was possible to block the affected modules. If that were not the case, what would you have done, as a sysadmin?