This is nonsense. This won't solve anything until the relays themselves demand PoW from everyone. But even if it is - phones will do PoW, and spammers will do PoW on servers and they will still shit everything with spam.
Discussion
Paid relays are almost the same PoW. What difference does it make how to spend satoshis - either on PoW in equipment, or to pay for relay. In addition, phones will always lose to powerful equipment from spammers.