I kind of disagree with you, in that when I think about the standalone meanings of the words in each phrase, I think they do say the same thing.
The meaning of the words “You are welcome [to the help I gave you]” implies, to me, that there wasn’t actually anything to offer thanks over. You’re acknowledging their thanks, but telling them that they are welcome to take/use whatever it is you’re talking about. [EDIT: normally when someone tells me I’m welcome to something, I feel less compelled to ask and thank in the future. “You’re welcome to anything in the fridge”, for example.]
It does not imply, to me, that I would appreciate them returning the favour. That might be implied meaning in the phrase, but it’s definitely not what those words mean by themselves.
In any case, “You’re welcome”, “no problem”, “no worries”, etc… are all idioms that mean something different than what their individual words mean. The phrases as a whole carry a different meaning than the words themselves suggest.