I suppose this has to do with time and money. Phone calls and email are quick and cheap, and the websites help to organize large events by tracking RSVPs and creating buzz around who is attending. Because people are busier these days, hand-writing an invitation to someone you're not sure will make your event is perhaps more investment in time and money than we want to spend.
Still, I miss the mailed invitation, especially when I see cool examples like the one pictured above from Cotton Flower Press in Portland, OR. Like receiving a handwritten letter, a paper invitation brings a little ping of excitement to my day and elevates the event, even if it's something as simple as a barbecue, to something that feels worthy of attending.
(Image: Cotton Flower Press)