Gradients would impose a significant burden on the bureaucracy. It's already complicated enough to figure out where a person's unique circumstances place them on various thresholds. Add gradients and the complexity grows exponentially. The net result would be a 100x increase in the number of public servants.
I don't think you should be getting downvoted, you are right. I don't think it's "100x more", but more complicated rules require more resources dedicated to their management.
It's one of the reasons people push for UBI. Welfare programs waste a lot of money trying to make sure the "right" people are getting it; UBI just gets rid of the waste.
The solution is simply: Make school lunch free for every student.
100x? I think this deserves a bit of a deeper insight. The inputs are the same, which means the verification steps are also exactly the same. The only change might be volume, but I highly doubt it would be 100x.
Outputs would change from bool to float between 0-1. That much is relatively easy given a calculator.
You can reapply whenever your income changes (and generally you are obligated to report such). At least in my state, the system to do so is mostly automated, although they do have a caseworker manually review such things. A good deal of people who receive government benefits aren't filing taxes at all, and they qualify for programs based on other proof, like a pay stub.
I think steep gradients are OK, as long as they are not over 100%. When someone is working and earning very little, they need all the help they can get. As they earn more, they need less help, and should start to shift to instead contributing to helping others. There is probably some ideal "ramp" that provides the right set of incentives. I think 75% is probably too high.
why? income number input results in output number of support. or you know it could just be a of their part time income % with a fixed min and max. or something like a reverse income tax.