I don’t think it matters since all lightning payments would go through the mint lightning node right?
Discussion
The problem is if the mint has high fee on inbound hops, or outbound on the next hop
Yeah I don’t know how to check that if the mint is private other than testing a payment.
Probably they have a private channel with nostr:npub1jluy3twvf338v6zlujzzdhjkzjy8ezj34ksydr8vw8a6jwp89ygshpp2kq , or use it with blindedPath