So, a turn server?  Very little info about the architecture here, but since you said relay operators would hate it, now I'm wondering why would I hate it?  Don't see a reason why.. 😎 The thing is, I know you can't do this without servers to bounce the traffic, and push notify uses too much Google servers to feel very OSS nostr.  If you keep your server stack opensource and configurable then relays can help run the network and decentralize.  If not, you're gonna lock yourself into being the one server and I don't think you really want that..

Turn services would be a really cool concept to nostrize to facilitate P2P connections.  I'd run some along side relays for sure, because then I don't have that data resting and clients can p2p any number of things..