Free higher education works well in the European countries that offer it.
What better investment could a society make than allow someone to pursue a field they are passionate about, and letting them start life with a clean slate? I'm by no means a socialist, but I think university should mostly be free.
The only thing (student) debt does is tie someone down. To a lifestyle or employer that they actually should have no loyalty to.
Tax brackets don't need to rise, resources just need to be moved from alternative things (i.e. military spending).