That’s only true if there were airlines that charged the minimum and would have charged even less in the absence of the regulation. The existence of the regulation is not proof of that alone.

The existence of the regulation is evidence of that in itself, because the alternative would be that someone for unexplained reasons put in the time and effort to pass a regulation that has no effect.

There is no law of nature that says all regulation has or had a purpose.

Which is why it's evidence. The presumption is that it was enacted with a purpose rather than without one because the vast majority of legislation is enacted to bring about some intended effect. To rebut this presumption you would need some explanation for why this legislation is an outlier.

I mean... you think that it was just random coincidence that essentially every single airline charged exactly the minimum fare?

Say... would you be interested in a bridge?