P2P connections is a place that's generally terrible for mobile. You have to keep connections open to more devices, which is generally bad for battery.

You could imagine a copy/paste that waits for a message from the cloud (because Apple push notifications are pretty solid), then opens the new connection to the local device, so the data never leaves your network. At least to me, that sounds needless complex when the typical use case could just send the entire payload with the "go look for this device" message.