I think it's somewhat generational and perhaps gender influenced, too. But also, an invoice is business correspondence, so I would expect that's also why. Sometimes I'll get CS responses from various businesses and they're signed in, to me, bizarrely informal ways that make me roll my eyes!

I never exchanged e-mail with former T while in therapy. And his invoices came by post on a standard office supply invoice form. Since therapy, social e-mails he signed "Take care" or "Till later" or "Fondly." I've done the same, with the exception of a condolence letter.