There is a problem with that though. For instance, if you're on foodstamps right now, and gas is not cheap, or it's very time-expensive to make it to the grocery store too often, then you're making single large trips. A continuous stream doesn't gel as well with that situation. You'd need a more comprehensive solution, like getting rid of food deserts in poor areas.
Or at least, if you're going to do this, you'd have to be very careful to not overcorrect for the 1st of tha month problem.
Not to ding your overall idea, I like it, think it's very cool. Just, to implement it with current infrastructure it would require a lot of care.
(Actually also I think rent or other large payments are less of a problem in your solution than you think - for anything on contract like that, you could simply reduce the rate at which continuous income is obtained. If your basic income is 100 units per whatever, and your rent is 43% of your basic income, you just reduce the stream down to 57 units)