In an enterprise setting, treating one level of logs as actionable, as GP mentions, is a very important for clarifying responsibilities.

If it takes the right pair of eyes on the logs to see a problem for what it is, the whole process slows down and doesn't scale as high. All errors and very chatty warnings should induce me to ask someone what's going on, to make sure it hasn't slipped through the cracks. And they should thank me for pointing it out. Otherwise you reinforce some bad patterns.

What does recoverable mean though?

If the server process handles it without crashing, is that a recovery?

A more general distinction IMO is the one presented in the article: an Error is something that should not have happened. A Warning is something that maybe should not have happened.