The main downside, in a nutshell, is inflation. There's simply no way to distribute the same amount to everyone in an economy and not have proportional inflation occur--because basically what you've done is dilute the value of every dollar in the economy. This is essentially what has happened with the cost of college. The more aid we give students, the more colleges soak it up...which leads to those who needed assistance still needing assistance as much as before, but the absolute cost of education has just risen.
Basic income sounds like a great idea until you realize the above.
Careful. Aid to students isn't something we can turn around and spend on something else when prices go up. That is a very different dynamic than "dollars I can spend like anything else". People bidding on status symbols with someone else's money, versus people trading off their various wants against each other from their increased-but-still-limited pool of resources.
I think you would still see some inflation as typical demand for the marginal dollar falls, even if you don't increase the total number of dollars, but it wouldn't look like student aid.
For the record, I support a low (certainly <$15k, probably closer to half that) Basic Income.
I don't think any of the BI proponents suggested to finance it by printing new money. More likely taxes, but keep in mind that they wouldn't be spent by the government. But speaking of inflation, in the eurozone, they can't seem to figure out how to increase it. Everyone seems to be anxious about the possibility of deflation. Which seems strange, because if they just printed money and distributed it to everyone, you'd think this would both produce inflation and increase consumption, no?
Basic income sounds like a great idea until you realize the above.