I grew up in the days of 2400 baud modems and even ran a BBS briefly. At the time, ASCII art was the only thing you could do to differentiate yourself.
Nowadays I suppose it's a combination of nostalgia and ease of transferring since pretty much every system ever has a way of reading ASCII.
But I wonder how long the trend will last -- the majority of internet users don't have "nostalgia" for ASCII anymore [0] and there are at least a few image and video formats that are becoming almost as ubiquitous as ASCII readers.
[0] I was recently on a discussion with some folks I used to work with at university about how our old workplace was no longer offering shell accounts to the students because they weren't being used. This made us all sad since most of us learned all of our command line foo at that workplace.