Is it possible to do that?
Yes and no.
Yes: it is possible to
1) create hard-fork or alt-coin with another protocol
2) use P2PK outputs instead of P2PKH outputs. This saves some space
3) use compression while storing tx data on hard disk
No: it is almost impossible to
1) change the current consensus protocol
2) use P2PK outputs instead of P2PKH outputs because all software works with addresses, not public keys
3) use realtime compression of blockchain because it is economically unreasonable
OK, everything is possible. but this is not reasonable.
The question is not about P2PK and P2PKH.
We can recover the public key from r+s with rec_id, and verifying this with previous output address will be enough.