If I may give you food for thought: I don't think you're right here.
It is a famous saying, and true, that "anything may be rationalized". What is "rational" may float, and indeed always floats, depending on both the situation and on who is doing the judging.
What underlies freedom? First, that it is endowed upon us by the same Creator that created every last bit of matter and energy in the Universe/Multiverse/Creation. In other words, the Creation was done on purpose, hence life was created on purpose. One (some?) of those forms of life are created in the likeness and image of the Creator, and He has given that life something that no other part of His creation can take away: freedom.
I can understand how that latter half can be a bit hard to swallow, but here's the thing: societies that reject this philosophy, and try to run on only empirical logic, fail. Look at ancient Greece - they recognized that there was a "prime mover" that kicked off all of creation, and they excelled at logic and philosophy. (Yes, there were "Greek Gods", but later they were all rejected by the ruling class.) What happened to them? They became the "intellectual slaves" of the Romans.
What else underlies freedom? The sacrifice needed to protect it. Sacrifice is almost never "rational" - indeed, it goes against the very notion of self-preservation and wealth accrual. Those sacrifices are made by people, on the whole, who recognize just Who gave us that gift of freedom, and would rather do His will than enrich themselves.
I love logic, but I find that it is so incomplete to form a beautiful society. Trying to understand God, as described by Christian / Jewish texts, can show how a balance of logic, wisdom, and sacrificial love can form the legs of a beautiful and lasting world.
Response: If I may give you food for thought: I don't think you're right here.
I don't hold with any claim saying that irrational values underlie freedoms leading to prosperity.
A+.