I've added to my post above, but in answer to that part.
You say that you test on 4x devices a lot, throughout the day. Do the tests provide you with feedback about that App that you then act on? It sounds like your testing schedule is too tight. Do you really need to test on 4 devices in one day? I don't think I'd see the benefit, but then again I think your Apps are in a different category to mine.
When you create a game, where most things are visual, I think that's important to test on different devices frequently (not every time of course, but once my devices are connected, they stay connected). Two recent examples (in both examples, the issue only occurred on a single device):
- my 10" tablet introduced a noticeable latency before displaying each menu because of the time needed to load some resources from the assets folder (as the changes to fix this issue were important, I'm glad that I noticed it at an early stage of the app);
- on a 4" phone, the size that I chose for the font did not allow to read easily (depending on the case, changing a font size can have a big impact on your app as you have to resize many objects); another font was fine on 2 tablets, but on the third, it was a bit ugly because of the density of 160dpi.
If you have very similar devices, testing on all of them is useless most of the time, but on very different devices, you can see interesting things many times a day (for example, a Kindle device from Amazon runs under Fire OS, a heavily modified Android, so it has subtle differences that you have to take into account). Testing on different devices is usually useful to check your layouts and make sure that everything is displayed at the right place with the right size, with the expected rendering, and also to check performance (imagine that you build your app upon a library that runs fine on your main device but is terribly slow on another device; what do you do when all your code is based on this library?).
EDIT: I never said that I wanted to install the APK on all the connected devices after each compilation (50% of the time, I test only on one device). I want to do it easily every time I need to, and it's many times a day.