Spotify is the company best positioned to fix this, although I'm not sure they'll be able to.
The real issue is that podcasts run on old backends like RSS, and there's no reason for creators to change that without a functional platform to offer a financial alternative. With the current format, creators embed the ads and all's well. Even if a lot of users skip the ads, some still here them, and some go to the affiliate link.
With an alternative system, like Spotify, there's the possibility of a better system. Spotify could host a network that allows creators to separate their content from the ads, and then Spotify can distribute the podcasts via their app, with an ad-free version going to paying customers. Furthermore, if Spotify manages the ads that get embedded, they could insert ads that are more tailored to the listener. The added benefit (for creators and advertisers) is that Spotify could use the app to ensure that listeners can't skip the ads when they're listening with an ad-supported account.
I've been a proponent for a refresh of the podcast platforms for a while now, and even pitched this idea of a more subscription oriented model to friends who have the ability to build an app or service capable of this, but the reality is that it requires buy-in from multiple creators for it to be viable. As I see it, Stitcher and Spotify are the only two businesses positioned to make it happen, and Spotify (with its recent purchase of Anchor and Gimlet) is probably the only one with any legitimate interest in going this route.