As a user, I tend to disagree. Finding the store full of knock-offs that just are a skin over a YouTube channel is frustrating when looking for actual content and not a simple YouTube skin. He's not the first guy to make this YouTube-wrapper app, there are a lot of them. Too many.
First, this sounds like a problem the application store provider needs to solve with an improved interface, not nuking anything they don't personally find useful from orbit.
Second, what's "actual content"? Official content only? Undoubtedly some people who searched for "top gear" were looking for exactly what this guy put out.
I think its fair to ask why you can't get human intervention on these kinds of problems and for Google to _at least_ consider what happened was an honest mistake and not something intentionally attempting to damage other peoples trademark (or whatever).
That's another trouble with so many of these mega companies now that don't seem to have any kind of instance of customer or end user support at all. It's easy to code auto response systems, and bots that track down spam and malicious software, but to get an actual person to review what is being done is nearly impossible.
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".
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.
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.