Unix won because it was free? It is to laugh.

No, the alternative was generally the hardware vendor's proprietary OS, and it was usually LESS expensive. You typically bought the hardware, got the vendor's OS bundled, and then had to buy an expensive Unix license. You paid more to run Unix, at least as far as the actual software cost went. (This obviously wasn't the case for systems that only ran Unix and had no proprietary OS, but those came later.)

It's possible that the TCO of the system running Unix might have ended up being less, but that would be hard to determine. I'm just talking about the licensing cost.

Unix was neither free nor cheap until BSD 4.3 or later.