My suggestion to the developer would be to talk to the Pocket Casts people about offering the desktop client as an in-app purchase and share those revenues (easily traceable) with the dev. Maybe they could create a special authorization key that would allow access to the unofficial API without locking that account. The app gets a desktop version and the dev gets some revenue for his trouble, and Pocket Casts has some increased income to support any additional load on its servers (plus profits).
Just a thought. Tell me why I'm wrong / horribly naive / etc
One snag may be the collection of metrics. Marketing people seem to have realized that there's a burgeoning market that they haven't destroyed yet and they seem determined to correct this oversight. If they decide that they need to monitor listeners or make sure they can't skip ads, then third party clients are going to never happen.
They already make people pay separately for the web version (even if you already own the Android/iOS one), but it's understandable that there's much less people listening to podcasts on desktop, so they think it's not worth developing a proper desktop app.
My suggestion to the developer would be to offer the app to Pocketcasts for a fee based on his daily rate (to cover the time he took to wrote it) plus a reasonable royalty percentage per year. He could then have his app, not need to maintain it at his own cost and possibly make a bit of cash from the royalty. If the Pocketcast people give it away for free, he makes only the dev cost back - but doesn't lose much really - but he gains the app he wanted.
The only thing I don't get is why the desktop version would be an IAP of the mobile one, that makes no sense.
Though it would probably have been a better idea to do that before they discover you've spent the last week publicly tweeting about unauthorised use of their internal API.
Just a thought. Tell me why I'm wrong / horribly naive / etc