I agree with your overall statement that government assistance is only "welfare" when it's means tested. Welfare to me has a narrow definition.
I've seen people on here say that deducting interest for mortgages on your taxes is a form of welfare.
As far as deducting morgage interest, that's not means tested, so it's not welfare, although it is a subsidy.
What I don't like about it is that it is as much a subsidy to the bank and the construction company and the real estate agent, as it is to the home owner. I don''t believe in subsidies as they distort our economy. Of course I don't support means tested welfare either.
I have no issue with providing for the profoundly handicapped however, or for infrastructure or protection of life and property.
Americans are so enamored of equality that they would rather be equal in slavery than unequal in freedom.
Alexis de Tocqueville
"Small people talk about people, average people talk about events, great people talk about ideas" Eleanor Roosevelt