We definitely need something like this because some people don't know how to install apps directly themselves or how to unlock their phones to install 3rd party apps - but you'd have to find a way to get your app around that too. Also the new Google Play Security feature blocks apps where they don't recognise the keystore file - so that again is something that people will have to turn off or know how to skip - or you'd have to make the app available on Google Play as well and I don't know how many hoops you have to jump through to release such an app in their store - or if they will still allow it.
Problems I foresee:
My views for Android games here, at itch.io are pretty much non-existent, so I don't know what the market is like.
The one or two games I did download from here for Android were very disappointing - they were the type of games where the developer is trying to maximise their earnings at the cost of having a playable game - i.e. you only can play for about 5 minutes before you must watch a full video ad or buy something, one of them also had major bugs in it. It's put me off from trying the Android games here. Itch.io doesn't force people to tell you if there is advertising or in-app purchase and then after you download it you get a nasty surprise when that's pretty much all the "game" is about. With the results that, as a developer, I'd love such an app, as someone who plays games, I wouldn't use it - I'd go to Google or Amazon where I know upfront if there's advertising or in-app purchase in the game.