Of course there is a problem that chain code / master is sometimes known by the wallet providers, etc.
If your master private key is already known by your wallet provider, then your coins are already unsafe and could be stolen at any time. Quantum computing doesn't change this.
and also who will distinguish which coin is a part of HD wallets/which not (and thus which coins can be locked for ECC signing).
This is impossible to do. You either lock them all and accept that some of them will remain locked forever even if the true owner returns, or you lock none of them.