They sell both ice cream bars and popcorn here in Toronto. Although i don't like eating anything while watching theatre at all (don't like the distraction), I would much prefer that those who do choose ice cream over popcorn, for several reasons. First of all, as others have said, it is much quieter. I have been seated next to people who buy popcorn and rustle it around repeatedly to grab some in their hand, and then crunch on it loudly while chewing it, and then repeat that process for an hour. It is exasperating. Ice cream, on the other hand, is quiet while being consumed, and the fact that it is at risk of melting encourages people to finish consuming it while intermission is still going on or within the first few minutes of act 2, rather than saving some of it for later during the second act (as with popcorn).
I've never encountered spilled ice cream in over 8 years of frequent Toronto theatre-going, as generally the age of people old enough to enjoy live theatre tends to be high enough to be able to enjoy an ice cream bar without depositing some of it on the seats or floor. People will take young children to the cinema at an earlier age than to the theatre, since the latter is much more expensive, so generally most people wait until the child is really old enough to handle a long performance, and in that case, they are old enough to manage ice cream cleanly as well. And the intermissions are long enough for most people to finish anyway, and then they can wash their hands afterwards if needed.
One thing that i do sometimes buy at the theatre, either beforehand or at intermission, is coffee, and that is something that i really miss when i am seeing Broadway shows (except at the Lincoln Center). If i haven't had much sleep during the week that i see a show, it is nice to have coffee there to help avoid falling asleep during a show that i want to see. Beforehand, there are plenty of coffeeshop options(!), but at intermission, it would be nice to be able to get a cup of coffee in NYC the way that i am accustomed to doing in Toronto, but hey, can't have everything. And while we're on that subject, being let into the theatre more than 5 minutes before curtain when you arrived there to get in line more than 20 minutes before showtime would be an enormous improvement over how many of the Broadway theatres are run. Only the Gershwin and Lincoln Center seem to get this right of the Broadway theatres that i have been to (which is actually now all of them). But i digress.