No, they wouldn't. Source: go back a couple decades, and student loans had low interest rates and were dischargeable in bankruptcy. It was an option. And, in fact, practically nobody did that.
Spherical cows. You are applying economic theory in a vacuum. Sure, we joked at the time we could just declare bankruptcy and keep the degree. However, show me sources showing that this was a real problem. It wasn't.
Simply, people were not playing the game that way in any serious way. I am pretty sure I have never met a single person who declared bankruptcy purely to avoid a student loan.
People might not do it for a $15k loan (accounting for inflation back then), but they definitely will for $100k today. School was much cheaper back then.
Student loans are still dischargeable in bankruptcy to this very day, but there are restrictions.
Those restrictions started being introduced in 1978, so more than a couple decades ago.