The "you have to do it properly" part also applies to moving BTC thru Cashu, Lightning, and Coinjoins as well not just Monero...

The major problems arise from Bitcoin on-chain itself being transparent

Cashu and Lightning are functionally different currencies and don't inherit on-chain network affects. I can't send on-chain Bitcoin to your lightning invoice. I have to get sats on the lightning network first somehow. Just because a merchant accepts on-chain Bitcoin doesn't mean they accept Cashu or Lightning. It's very likely that they dont.