What's your source for saying that most people fail to understand that social welfare programs come from taxes? The concept of where government money comes from is such an obvious fact, I don't understand how you can claim most people don't understand it. People go to work for a paycheck, they pay taxes, and they understand money doesn't grow on trees. This is adulting 101.
And no, "subsidized" means a portion of something is covered by someone else, but not necessarily all of it. E.g. a subsidized cafeteria at work may mean all the food is 50% of cost. Subsidized can mean fully subsidized, but that's a special case.
So subsidized is not more precise, it's actually much less precise. "Free" continues to be the accurate and correct term.
You're taking a right-wing political stance against current levels of social spending, which is your prerogative, but there's no need to change perfectly fine language to do so. Even if we called it the mouthful of "fully subsidized childchare", that's not going to make it any less popular.
And no, "subsidized" means a portion of something is covered by someone else, but not necessarily all of it. E.g. a subsidized cafeteria at work may mean all the food is 50% of cost. Subsidized can mean fully subsidized, but that's a special case.
So subsidized is not more precise, it's actually much less precise. "Free" continues to be the accurate and correct term.
You're taking a right-wing political stance against current levels of social spending, which is your prerogative, but there's no need to change perfectly fine language to do so. Even if we called it the mouthful of "fully subsidized childchare", that's not going to make it any less popular.