It's trivial to connect your lightning node, and so its channels, and so the UTXOs. Just signing up to Amboss, you've doxxed all your UTXOs. Being a good lightning node operator and linking contact details to your node, you've doxxed your UTXOs. To what extent is this important? That's an individual judgement.

Any UTXOs that come from my node and will eventually go into cold storage, whether from closed channels or a swap out, eventually get a whirlpool first.