The only way to have a pure payment system and nothing else (zero arbitrary data) is with MimbleWimble (GRIN, BEAM). Even Monero can store Ordinals:
https://mordinals.org/FWIW it's possible on Monero mainly because it has TX_EXTRA field which sometimes used to interact across different cryptocurrency network.
Reject block? No sane people would do that since the block contain some non-ordinals TX. His script would make sense if it doesn't relay all Ordinals TX.