You trust it with the ability to sign stuff on your behalf, but it doesn't get your key. You can remove its access anytime you want. The entire point is to allow a kind of delegation that doesn't require lending your key to others, nor breaking the network (other people don't have to know you've setup some arcane and stupid delegation mechanism). But yes, like any delegation mechanism (and any of the dozens of delegation proposals we've seen in Nostr) at the time you delegate to someone, they are trusted to some extent. The magic of Pomegranate is that you can revoke that trust any time you want.

It is perfectly possible for an operator to independently get your approval, or apply a rate-limit, a time limit, a kind check, anything it wants. There are currently two implementations of operator servers out there, but there could be many other variations and people could pick the ones they prefer. If Nostr and Pomegranate get more popular I expect to see lots of these servers out there with different policies so everybody can be happy.