Welfare goes back well before 1800. In western Europe it was the responsibility of religious groups to run the program and gradually the government took over. For many years “welfare” involved waiting until the person was down to the clothes on their back and nothing more, and giving them food and shelter in the “poor house”. The switch to “home relief” (giving them money so they stay in their houses) was largely 20th century, and has proven to be cost effective.
There is the halachic issue involving taking charity from goyim. There is also the issue of whether it is counter-productive to give people able to work money rather than jobs (this is best observed by noticing how employment among able-bodied persons over 65 has radically fallen since the government started paying them not to work, and continued even after unemployment ceased to be a condition of receiving social security). This is especially a problem now that most industrialized countries are facing serious labor shortages.