How do you let people know about the website? Social media posts? How do you contact people not on social media about the website? A mailer? A phone call/text? These are just questions I would ask to understand why paper invitations are still a thing. Rather than providing a self addressed stamped envelope for the RSVP, just put the website into it.
Also, people love to hang things like invitations on their fridge as a constant reminder of an event that's somewhat far into the future. Rarely is that something printed off of a website, but a card received in the mail will pretty much get placed there straight away (or maybe after sitting on the counter for a period of time).