Here are some issues it would have caused:
(a) Reduced my chances of getting an education at a top rate university (because I would be considered "at risk" for not succeeding, at least on paper). So I would have ended up at a less prestigious school, made less money, etc.
(b) If I had say 10% of my income siphoned off to a private company (which is a scary thought), I wouldn't have the opportunity to choose how to spend my money. For example, I have chosen to skip paying a loan payment to pay rent. I called and asked if this was alright, they told me it was fine. It kept me from being homeless for a month while I handled a cashflow issue.
(c) Because of the tax benefits, I have zero incentive to pay off my loan quicker. If 10% of my income went to some loan agency I'd pay it off quicker than I am now, and thus have less interest to write off. Further, I make money quicker than I lose it due to loan interest on the stock market, so I can actually pay back my loan faster by investing, then paying down the loan. This also helps spur the economy along, and at scale this is a massive reason it's not in anyone's best interest to implement a plan like this.