In my personal opinion, it's better to display the username than the NIP-05 alias.
Discussion
Username is not unique, better nip05.
NIP-05 is misleading.
It's not verification per-se. It's just a DNS alias.
I understand, but I believe it's PoW
Sorry, it has nothing to do with PoW.
It's delegating the identity to a third-party most of the times.
If the domain is owned, I believe there is proof of work.
It's just proof that you have access to the domain. There is no verification.
You have access to the domain (and a webserver and a certificate)... or you are using a third-party service and you are trusting them with managing your identity.
And I would say most of the time it will be the former option.
Either way, I agree that something has to be done.
That doesn't make sense:
It works fine.