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At least the DMCA takedown wouldn't also somehow disable his google music subscription.

That's a problem with bundling services under a single account, not with the closed-ecosystem part. For example, GoDaddy suspends all your sites when you get a DMCA takedown to any single one of them.

I agree that the approach is bonkers, but it's not an issue exclusive to "walled gardens".

Actually no. The DMCA is a nationalistic piece of absolute garbage, but it does allow you to file a counter notification, google does not.

If you were on the open web, his app would be a page with youtube's embed code for each video.

I doubt you would use a DMCA takedown request for this. You'd just disable embedding of your videos in your youtube options. Youtube probably already knows when a video isn't requested from either youtube's website or the official youtube app.

Mentioning that venue B is screwed up, is hardly proof that that venue A being screwed up, is a good thing.

I'm not saying it is a good thing. I'm saying it's not a problem caused by "closed app eco-systems". Trademarks apply to both closed and open marketplaces.