I don't think I've ever received an invite to a casual event over text/email/phone either, except in conversations of the "Hey, what are you up to?"/"Going to a party, want to come?" ilk.
I just text everyone I want to talk to.
Maybe it's because I went to a decently sized high school (a little under 2000). Or maybe it's because I currently live in a large city (top 20 populated city in the U.S.) Or maybe it's because I'm an extrovert.
But I would probably be overwhelmed by the sheer number of events my social network would produce on FB. I already accompany friends to events thrown by friends of friends pretty frequently.
How often do you go to these birthdays of people you barely hang out with? The average person has like 300 friends on FB. The median number is about 150-200. That's a lot of birthdays.
So if I left Facebook I'd either never know about any of what's happening, or everyone would have to go out of their way to invite me especially, which I don't see as a viable long term thing for me or for them, over time they would increasingly forget to invite me - I've seen it happen with others who've tried to leave and had to return to get back in the loop!
Plus even if I posted to say that I was leaving Facebook my post wouldn't be seen by everyone so they wouldn't know, and if I disabled my account the post would disappear altogether.
So I'm locked in for the foreseeable future out of social necessity.
PS - I've never heard of Evite, until I just realised I thought it was being used as shorthand for an electronic invite, not an actual website.