Noncustodial wallets want a reliable UX which generally relies on the LSP being stable and reputable, which sadly means not Tor and generally requires them to be large for profit companies.

Tor latency is not ideal for order routing.

Is it possible to have an LSP that is *only* accessible by TOR/onion address, and *not* available by clear net?

What if all routing was on TOR with no exit nodes or clear net required? Build it and they will come?