I like to think of DELETE as "if the response to the DELETE is 200-level then further GETs to the resource should be at the 400-level." Call those responses to GET requests "2XXing" and "4XXing" respectively.

Similarly a PUT should make sense whether the underlying resource 4XXes or 2XXes, and should in either case make it 2XX with the same response.

Then POST is just a verb which does not share these semantics at all; POST <url> can be done on a URL which either 4XXes or 2XXes, and even if the post succeeds that's no guarantee that the underlying URL will now exist. POST /update-caches for example might not change the HTTP statuses of anything.