Instead of paying with loan money or hoping for grants, anyone could go if they will give up (for example) 10% of all future income (this is not the same as "income-based repayment.") Instead, a system like this would have whoever is buying the shares (I'd prefer it be universities themselves) give you a full ride (not just tuition, but books, room and board, transport, food, etc.) and you'd pay them out of your gross income after you graduate. The big difference is that just about anyone who is willing to give up the percentage could get it. Sticker shock and rising bills do not come into play. Right now, you're at the mercy of the financial aid system and all its fickleness (relatives make too much/too little, you have too many/too few assets, you are in a high CoL area and loans don't cover anywhere near what you need, the amount they're willing to give you shifts with the political winds, etc.)
The advantages of this system are that you would never have to worry about your relatives being able to fund you; you wouldn't need to work while going to school; you would not need to reapply each year and hope you get enough; and there's no issues with bankruptcy or anything else (the obligation would be non-dischargeable, just like now, but since it's a percentage, the sting is much less.) Instead, the money would all be there the whole time.
On the investor side, it would be like VC: most people would produce standard returns (let's say 5-15k a year), while a few Elon Musks and Larry Ellisons would return billions - I'm sure many universities would be happy to occasionally get one of those.
In any case, there's no way it could be /worse/ than the system we have now.