Linux is one of the cases where the difference matters a lot, because /dev/random is blocking. I think it's BSD where the two devices are the same.
I like how you put that. Best way to because infrastructure reliability is way too important to sacrifice over questionable security gains. Puts a QED on the whole discussion.
In practice, that's rare, but some consumers have strict, hard requirements that can't be ignored.
Retrieving output bytes doesn't change anything.
The view "take three bytes output, lose three bytes entropy" is simply not correct.
[1] That is, before enough external entropy has been gathered.
All of crypto relies on being able to generate an arbitrary amount of good random bytes from a single 256-or-whatever-byte seed. Otherwise it wouldn't be safe to encrypt a long message with a short key.