their whole shtick is that Poland is infested by traitors who need to be excised from society....
This much is true, however it's a sad fact that a lot of people need enemies or bogeymen even if imaginary. Just look at some of the people who post here.
I'm in general in favor of welfare but it has to be well managed
Agreed, however given that the state (whichever country) are rarely ideal at managing things, I'd rather err on the side of generosity to the poor than stigmatising them.
a little embarrassed
That's almost the opposite of the truth. Child benefit in the U.K. (can be compared to 500+) worked as well as it did because everybody got it, rich, poor or in the middle. This was partly to eliminate shame, something mitigated by every woman with kids in their community from the lady of the manor to the roughest semi-homeless woman and everything between those poles queueing up together for it in the post office. Fishwives could gossip however they'd never truly know if the woman in question needed it to feed their kids or spent it on having their fur coat deloused.
If it hadn't been universal, certain of the families who needed it would never have applied for it and their kids' futures would have been worse off for that.