I wouldn't put Allen anywhere near those names.
If you look at his past one year sample, as Bellhorn did, he is good, but he's also been as effective as plenty of othet lesser names, like Dan Otero, Addison Reed, Tyler Thornburg, Mychal Givens, Matt Bush, etc.
He's a good reliever, but he isn't some special commodity that enables Cleveland to operate their bullpen differently. Francona chooses to do so because he's a brilliant manager. Oakland is basically doing the same thing with Santiago Casilla facing the tougher hitters and, if there is still a save to be had, then it goes to Sean Doolittle or Ryan Madsen (lately it seems to be Doolittle).
None of them would be considered elite relievers at this point in their careers, although there may have been a time you might say that about Madsen or Doolittle, but injuries have changed that. ..