College is different than food. Everyone cares about going to most prestigious school they can afford (that will accept them), which creates a bidding war. This is actualy very similar to housing markets in desirable neighourhoods - everyone wants to live there while there's room for maybe one person in ten, so the market forces set the price at a level beyond the means of the bottom 90%.
Food, on the other hand, is a globally traded commodity. There's no reason for the food prices in the US to go up if basic income was to be introduced there.
For college in particular, where it is quite specifically the fact that you are (better skilled and/or better connected and/or more able to pay) than everyone else that commands a premium this is very much the case - we can't just build more prestigious schools.
For housing, for most people, the bulk of what makes a neighborhood desirable is location relative to their work and social group and activities, cleanliness, and safety. Prestige is less of a component outside the very high end, where we don't care to subsidize anyway. The market (and the rest of society) can absolutely provide more "desirable neighborhoods" for the desires of the people who will be turning a net positive from BI.
Food, on the other hand, is a globally traded commodity. There's no reason for the food prices in the US to go up if basic income was to be introduced there.