Physical wedding invitations are still tradition such that people may get offended if they do not get one in the mail.
I personally abhor empty formality. I got married 10+ years ago and can't for the life of me remember what we did for invitations and I doubt anyone who came remembers either. I remember the food pretty well because it was great. We did a chocolate cake (black forest) which people still remember.
The formality isn't empty in the sense that it's purposeless: it's done for a reason.
After all, marriage itself could be considered an empty formality, so if you're going to bother getting married you might as well embrace the formalized aspects of the occasion.