I do remember the old days, including when bullpens featured a "long man" or 2. For that matter, I remember before Tony LaRussa invented the 1 inning closer.
Those days are gone.
I don't think it makes sense to dedicate a spot, and even if it did, I don't think we have any likely candidates. If a guy can routinely go 5 innings and routinely limit runs, he's a starter. If he can't, he's a 1 or 2 inning guy.
"Long relief" just isn't a thing any more.