My concerns here are:
* Making sure wallet applications can function without supporting the
P2P protocol (which drops a huge implementation overhead for simple -
perhaps hardware-based - wallets)

How would such wallets get transactions into their wallet in the first place?

The P2P protocol is really the simplest part of implementing a wallet, IMO.

I don't really have a strong opinion either way, but doing more work to prevent transactions being announced to the network feels weird.