This system, in a way, exists in the UK. We have a single (govt sponsored) source of student loans and repayment is taken out of paychecks automatically. In the pre-2012 scheme it's 9% of everything over £20k (roughly), where the median salary outside of London is ~£25k.

For me, my student loans were about £20k overall (including living costs) and I'm paying back about £2.5k/year from it. Most of my friends are never going to pay it back.

However, it's not really put much burden on universities as they get the money immediately and then the losses from non-repayment are absorbed by the government.