There are two primary things that cause this to happen in reality.

The first is that politicians want to get credit for creating the program, but also don't want it to cost a lot of money. Their incentive is to create a program that sounds good but does and therefore costs as little as possible. But making it obvious that it doesn't do much compromises the "sounds good" requirement, so instead they make a bunch of complicated rules and barriers that keep the price tag low but in a way which is difficult to understand. Relatedly, the people administering the programs are often under orders to accept some particular number or proportion of claims, again for budgetary reasons, and then if there are too many they have to start fabricating barriers themselves.

The second is that there is no accountability mechanism. Some majority of voters support the idea of the program, but they've been assured that it was created and exists and have no idea what a mess it is, and only a small minority are recipients. So if things are unintentionally broken, they don't get fixed, because the majority isn't aware of the problem and that's the only thing that gets politicians to address it.

It's not because of politicians opposed to the program. If politicians opposed to the program have a controlling majority then they simply repeal it. It's the politicians who support the (pretense of) the program who screw it up.

This is one of the reasons why complicated systems with many overlapping benefits each with their own application process and phase out rates are so ineffective, and the better way to address this is with simple direct transfer payments like expanding the EITC or a negative income tax.