Or do you mean in the abstract, fairy-tale ending sense?
And "EOL" is a convenient shorthand for those conditions.
Most use cases care about never getting patches for security problems ever again.
If the end user of the product or their needs don't matter, sure.
I dunno, a widly known RCE seems a pretty good reason to take something out of production.
Honestly, in that case I tend to agree with GP. As long as you recognize EOL means you are in charge of supporting it and possibly backporting security fixes and you're okay with that - why not use it?
In many cases it is not, it is purely a 'ticking time bomb' - if new CVEs or requirements arise which cause issues in EOL versions, you may not even become aware of the vuln.
In counterbalance, new versions of code have new, unknown CVEs, new bugs, etc.
The issue is that of support, the fallacy and process issue is that 'current' support is of greater quality than 'historical' support, or that old software has a disproportionately higher support costs than 'current' software.
The true issue is overdependence on FOSS software and unwillingess to contribute - all software has costs, major vendors are 'coasting' on work provided by free volunteers and panic when those volunteers decide to no longer work for free.
If vendors were doing the legwork necessary to properly inhouse their dependencies, I would wager that much less software would end up discarded in 'fear', for a lack of a better word than this - modern development is supposedly built on features and patches, any codebase should be maintainable for a much longer period than its supposed EOL.
Wouldn't it be a nice world where you can just declare something EOL and it disappears and somehow magically it's not a problem anymore for anyone end-to-end? Thing's just don't work that way. Like, suddenly, a product that was working perfectly fine for who knows how long suddenly needs to modified because some ass-hats thinks that EOL isn't suitable for production.
There are a number of reasons to upgrade a dependency or a product; an EOL label shouldn't be a part of the calculus. EOL may imply certain conditions that may influence the decision to upgrade but for the sake of EOL you can eat a bag of dicks. Think harder why you're proposing an upgrade is needed and how it'll add value to the business. EOL software is perfectly fine especially because it's been battle tested.
We also use log4j 1.x all over the place and I feel zero need to change that.