Postcard collecting is at least as well entrenched as sports card collecting. In fact, Burdick wrote books on postcards. I have two of them. And there are postcard shows all over the place, still.
As for whether they are worth collecting, I guess it comes down to what you like, as noted above. I think some PCs are as nice as anything ever issued in a pack of gum. Additional reasons to like them are large format images and often postmarks and stamps that help authenticate them. And some of the messages written on them by their senders are hilarious.

They also make nice autograph vehicles, especially when they are postmarked with the approximate date of signature or are from businesses owned by the celebrity:
And you can't help but love the graphics:
There's also a nice, er, variety of subject matter available: