VLS itself doesn’t deal with privacy, so like Tony noted this would depend on the privacy practices of the LSP or custodial app in question.

There are other setups, such as an enterprise running their own node(s), where they’d want to separate the signer for security. This provides them security both from malicious actors attacking the node but also internal employees, to allow for separation of duties between node operator and the person who can sign for transactions (or people once multi-sig lightning becomes a thing ⚡️)