I've heard back from the staff at TuneIn who confirm it's the stations, not TuneIn. Each station can do and is doing what it wants. Tesla is just using TuneIn's API, and TuneIn is dutifully fetching whatever stream a given station provides. It's the individual stations who are mucking around with their streams and in so doing, in my opinion, ruining the experience with all their promos and ads.
I remember something similar happening years ago when I lived in Silicon Valley. AT&T offered CableTV services, and one day they changed the firmware in their set-top box, so that an upsell/monetization blurb would appear as soon as you flipped from one cable channel to the next. Well, you can imagine what that did to the user experience: the interstitial ads killed the very notion of "flipping" between channels. It now took 3-5 seconds to switch channels. When there were, what, 200? 500? channels? I dropped AT&T on the spot.
The other downside of TuneIn, at least here New Mexico... as soon as you get out of range of cell towers, which is like a huge chunk of the state, no more TuneIn.