For shows that have empty seats, this is a great idea. Keeping the age low will encourage student audiences, without any need to pre-plan. I doubt it would seriously cannibalize most shows, since students aren't likely to be spending the higher prices (even at TKTS).
When I was at Columbia in the late 60's, International House on Riverside Drive used to have student tickets for selected shows available the day of performance for (hold your breath) 25 cents!!