* A bunch of reviews from users, very few of which sound fake: https://itunes.apple.com/us/app/overcast/id888422857
* Articles about the app from well-known websites: https://9to5mac.com/2018/04/29/overcast-versus-apple-podcast...
* A wikipedia article: https://en.wikipedia.org/wiki/Overcast_(app)
* Information about the developer: https://marco.org/about
You could fake all of this, but it would be really difficult and expensive, and probably wouldn't work in the long-term.
It's true that for a brand-new app from an unknown developer, it's difficult to say what their intentions are, but Google and Apple don't really have any more information to go off of than you do regarding that - at best, they likely have the developer's contact information, but you can probably find that yourself as well. Additionally, the nice thing about sandboxing and permissions is that you don't really have to trust the developer in order to run an app. For example, the other day I was looking for a protractor app that would give me measurements in tenths of a degree, and I found this app [1]. Aside from a few reviews (which, as you said, could easily be fake), I know absolutely nothing about this developer - for all I know, they could be trying to steal all my data. But because iOS sandboxes everthing, they won't actually be able to access any of my data or do anything bad unless I approve it, and if I don't like the app, I can press one button and get rid of it. As a result, I can feel comfortable installing the app anyway, even if I don't trust the developer.
Apple requires people to provide a business number among other things, and they have substantial ability to 'dig in' to a developers background.
Users have zero interest in this, and nobody has time to do some big investigation into some company for the sake of some app.
The whole point of the app stores are to filter through the crap for us and give us some idea of what's good and what's not.
I don't know why this business got banned. I assume it's due to the outsourced dev they used. I doubt they're technically competent and reviewed the app themselves, so who knows what kind of bullshit the dev stuffed in their or their other apps.
Wow - no, we do not have the ability to ascertain the overall trustworthiness of a dev, certainly not better than Google or Apple.
Reviews can be faked, and 'how long their app has existed' is not a very good measure of anything. Their T&C's on 'protections' don't mean anything if they are not already trustworthy.
So unfortunately, this is one of the valuable things that AppStores can provide.