I mean, if that were true, why doesn't every company only hire women?

I'm not going to debate the matter itself here, but this is obviously not how it works. There's no law that says you have to pay women less. When people say sexism causes women to be paid less, what they're saying is that sexism causes women to be undervalued by employers. Why then doesn't every company hire women? Because the average company doesn't think a specific female employee is underpaid, they think their individual female employees are paid less because they're less skilled than their individual male employees by coincidence.

Again, not going to debate the merits of this claim that women are underpaid, but the argument isn't that it works the way you say.