This is what's frustrating about America. There is so much bureaucracy that exists only to pay for itself, and I suppose, provide a few jobs, but you're an unreasonable socialist if you point out that it'd be cheaper just to not keep track of who needs to pay and give food to everyone for free instead.
No, it exists to prevent people from receiving public services, both by its direct operation and indirectly by making the service more painful to use so people who would be entitled to use it nevertheless avoid it.
But your second point is very true. It can be very painful to interact with the bureaucracy, something people shouldn’t have to deal with when they’re at the bottom of the barrel.
There's no reason it has to be.
> The people are supposed to decide through indirect democracy who is qualified to receive welfare.
There's no reason the people couldn't decide, through democracy (direct or indirect, as is their pleasure; certain existing governments only embrace one, but the people can always change that, too) that the answer is "everybody gets the public service/benefit; and the payment comes through the tax system" and have one tax bureaucracy instead of a tax bureaucracy and a separate eligibility verification bureaucracy for each program.
I guess, to steel man your argument, you could issue cryptographic IDs or have government offices with biometrics to authenticate. That would simplify some of the problem. I’m definitely not saying simplification isn’t possible—just saying that verification will always be necessary work.