modify close so that it automatically logged any errors

Yes, I think that would be better behavior, especially when close is called in a void context (like an "autowarn", like you said). The history of Perl internals is mostly to return success indicators but I think autodie is probably a better choice for most of them and autowarn is the best choice for close.

Basically, there is never a logical recovery step; because the actually failure that gets reported by close may have happened hours ago; and because the range of possibilities is so diverse

Not in my experience, no. The failures are all "incomplete data" and the likely mitigation step I already mentioned: Don't process that incomplete data. Additionally (as I already mentioned), don't mark the data source as "processed" if the protocol has such a step (which many protocols I use do).

True, the recovery for the root cause is not something that I expect the software to try to solve, of course. The mitigation is usually just "close ... or die ...". Somewhere up the stack some eval takes care of trying to mark the item as failed or just not marking it as successful (and deleting the incomplete file if one was being written to).

But my experience matches your expectation: that having close() autowarn would be better than having it autodie. Having close() autodie would more often abort further work when there was no good reason to.