I think these radio stations are pretty mercenary, driven by profit seeking rather than ideology. I think if there was a buck to be made, they'd play back-to-back female artists all day, every day. I assume the stations are (modulo basic incompetence) playing what keeps their audiences listening the longest. It's trivial to say "oh look, there isn't enough representation on the airwaves", but unless you have a convincing argument that more representation would bring in more revenue, why would they listen? The FCC is not going to mandate it on the basis of the public good, go ahead and put that out of your mind.
I think the point is that this is a self-fulfilling prophesy. There isn't much airplay, which makes the industry invest less in women artists, which in turn means there are fewer songs by women available to play, thus less airtime.
I would agree that it's not ideology driven, but there is a large risk that the stations are trapped in a local minima. Without more diversity of programming (and ownership), it's hard to know if the old rules are the most profitable rules. With media ownership consolidation, it's harder to add enough entropy to the system to really know.
And that’s the core issue here, media consolidation. Local news companies, radios, even some businesses you may not expect are all backed by large corporations that bulk-buy stations. It’s very hard to find independent local businesses in media because A) rich people love controlling the populace and B) a lot of this benefits from economies of scale, which is unfortunate. For instance music licensing, then sub-licensing, is a very good way to redistribute music legally.