It really can’t be compared to an average wedding. They were simply following protocol. The royal Big Wigs of Europe need to be booked in advance for things like weddings and also require being given earlier notice than those heads of state, general plebs and celebrities...it is custom to do this via fax. Regular paper invitations were sent out after.
We pretty much just use the fax machine in our office for super sensitive correspondences that could be intercepted via email (although I can see faxing being problematic as well, it is protocol and considered safer by the company). I definitely don’t have one at home.