The Obligatory Cthulhu Expansion
Innsmouth, Rock Stars, Shapeshifters, Robots, Halflings
For the longest time, I refused to own The Obligatory Cthulhu Expansion because of Madness and my belief that it breaks the game. This is a topic for another time. But I accept Innsmouth and Miskatonic University as playable factions because their Madness is solely voluntarily, and this base provides a lot of value even if the Innsmouth are not used.
Any faction that has extra minion plays will benefit from getting all of those minions back. In fact, most factions benefit from getting their minions back (not Zombies), and the freedom to not worry about overpaying in minions can be liberating. The Innsmouth can use Sacred Circle and Spreading the Word to rush this base quickly for four points. You can reclaim those minions and repeat the process, since the Locals can find themselves.
Fetch based factions like Shapeshifters and Rock Stars will benefit greatly from getting the minions back that can find their fellow minions. Particularly, the Groupies chain into each other and then all go back into the deck to be fetched again by The Monarch. This ability will override the Doppleganger, but that just allows his ability to be used on another base.
Robot and Halflings - I think their utility here is self-explanatory. But, interestingly, this is one base where third and second place are equally desirable, and you get your minion back anyway, so you have to be very careful about offering a free two points to a player here. This base is a large reason why I bought the Cthulhu expansion.