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.
* 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.
One other thing is that, at least in Apple app store, the review process catches use of private APIs which are in theory harmless but are not considered stable and could cause the application to crash if a minor update changes the way they work.
Excessive resource usage is already pretty easy to avoid - iOS will limit resource usage when an app is in the background, and show you which apps are using a lot of battery power so you can uninstall them. I would imagine Apple could expand this more by showing an unobtrustive notification somewhere with a message like "____ is reducing your battery life, would you like to stop it?"
Regarding private API's, if Apple's position is that third-party apps are not allowed to use them, they should just stop exposing these APIs to other apps completely.
Solving privacy issues is tricker, at least in the short term, although I think this should eventually be handled by government regulation. Assuming we can get fair and well-written regulation (which, to be fair, is a big if!), we could have clearly-documented rules that apply equally to all market participants, and aren't quite as clearly biased based on commercial incentives (although there would still be an indirect effect due to lobbying).
While non-malicious, jailbreakme.com seems to come back once every few years or so.
I know you mentioned disabling javascript, but browsers are also a really good example of this. Browsers run your code in a sandbox, and the rendering engine itself is sandboxed in case of bugs. As a result, you can pretty much visit any random website and know that it won't compromise your system - as far as I know, there haven't been any widespread attacks using browser vulnerabilities since sandoxing was introduced (except maybe Internet Explorer, which doesn't really count). The worst that can happen is that a browser tab starts using too many resources or doing something annoying (like autoplaying a video), and you can just close the tab and make it go away.