> because income requirements that cause people to fall of medicaid or SNAP completely are sharp

How often do pay increases perfectly keep someone in the gap? Presumably some of them will be large enough, through changes of jobs for example, that the family would completely jump that gap.

> because income requirements that cause people to fall of medicaid or SNAP completely are sharp

Why would it? This is perhaps intentional as well. Only allow the program to benefit half the country. I'm sure you can predict how that political split occurs and insulates politicians from the ballot box.

> It serves to have an underclass that politicians can dump on, it seems.

It helps keeps wages suppressed. Politicians want money. They don't care about "dumping" on you, they'll make any excuse they need to keep the money coming in.