It’s quite common when giving my email over the phone that my full name has already been established so I really wished the “Ø”-version would work (I also own that domain) but most (many? Some? Too many) email clients refuse to send emails to servers that contains special characters.
I can receive emails at the ø-domain, but not send to it using Fastmail. They recommend I use puny codes but that’s way too difficult to communicate.