Fortnite was the most ambitious attempt to distribute outside of Google Play. Here's what Epic had to say:
> After 18 months of operating Fortnite on Android outside of the Google Play Store, we’ve come to a basic realization: Google puts software downloadable outside of Google Play at a disadvantage, through technical and business measures such as scary, repetitive security pop-ups for downloaded and updated software, restrictive manufacturer and carrier agreements and dealings, Google public relations characterizing third-party software sources as malware, and new efforts such as Google Play Protect to outright block software obtained outside the Google Play store.
And Epic gave up and put it on the Play Store.