The problem is that a lot of mildly-interested students don't have the wherewithal to take the next step of calling the ticket office.
If it doesn't work like it should, they just don't show up (or they post on Reddit). Any barriers to entry for students will limit their likelihood to attend a game. How many students have tried to get their "free" tickets, were surprised by a $3.50 fee, and then decided to just not go?
I've been a season ticket holder for about 14 years now (before that was an undergraduate), but have also been able to utilize free student tickets for the past 6 or so years if I wanted (working on a MS). I tried once to get a student ticket through the app, and the hoops that students have to jump through to claim their "free" tickets for a MBB game are far too many. I wouldn't be surprised if it's a barrier to entry that many just don't even bother with.
I'm starting to feel like a Simpsons meme.