Or maybe the Tax office isn't equipped to hand out money.

I'm not joking here, but an office that has been focused on extracting money for literally centuries, with a strong emphasis on detecting fraudsters and sticking to laws and rules, doesn't have the culture to handle allowences for people in need.

The latter is a very human function. With lots of interpretations. The former is a very strict and rigid function.

which is why previously the latter was done by local authorities, often they even did it through proxies in the neighborhoods: something done by people, close to the people.