But only specific people will know about my domains used for specific payments.

Self-hosting LN address means you link a payment to that domain, that maybe you want to use it only in private, for specific payments.

Self-hosting LN address also means linked to a specific node, that maybe I do not want to make it public or linked to my identity.

I think you have limited perspective about what really is privacy. Privacy is not all about how to hide or avoid custodial, but is more not linking private info to public payments.

Custodial non-KYC ARE A PERFECT DECOY TO AVOID THAT LINK.