We've talked internally about making an Android app a few times, essentially doing something similar to what you're describing to create an installer. The short answer is it's very low priority and we're not sure if/when we'll do it. Our thought process about it:
- Since it would be an installer, it would have to live outside of Google Play. So a side-loaded third-party installer is already going to have a very limited user base.
- The amount of developers who upload APKs currently is relatively small compared to our other types of developers, so the amount of people who would want to use it could be pretty small.
- We've never built an android app before so there would be a lot of upfront cost getting everything built.
It's not off the table 100%, but it's also not something we have concrete plans to build in the near future.
Regarding an unofficial one, feel free to go for it. I would strongly prefer if it was opensource. Our API support is very limited/undocumented so you might have a hard time creating it. To do any sort of downloads you would have to refer to the itch app sourcecode to see how that API is used.