Oh, The Show can definitely be a barter-sink, too. But the thing is, they're actually strongly incentivized to obey whoever has their leash under at least some circumstances, and you only need to get them to pander once to pay for two or three sessions of even their most exorbitant expenditures (10 Barter is amazing).
A high Hot Show also doesn't mind pandering occasionally all that much (especially if their leash-holder is willing to aid them), and most Shows should get high Hot fairly quick.
The Show certainly can go down a path of destruction for everyone around them, but if they do, their leash-holder is very unlikely to want to keep them around, and that will generally result in them switching to a new one...and if they piss that one off too, then another, and so on until they've been through everyone. At that point, the incentive to kill The Show becomes very real, and with all the PCs in on it (or at least the minimum of two they've been bouncing between), they likely succeed. PCs, IME, are pretty willing to end a situation that's costing them 3 Barter a session for no benefit.
On the other hand, if The Show is reasonable and willing to do an occasional bit of pandering, they can easily maintain an excellent relationship with whoever holds their leash. And the better that relationship is, the more freedom of action the show possesses. It's possible for The Show to be indispensable without ever pandering, I suppose, but it's difficult.