Google doesn't have complete control. A significant number of Android devices ship without their store, and anyway, you can install apks with a checkbox in settings. Worst case, you ship to play store without this feature and mention in the support faq that you have to install the apk from a website download to have it.

Apple has slowly started to make things like that closer to being possible, but there are a lot more hoops, so it might be reasonable for a very niche app, buy anything you want thousands of people to use really needs to go through the app store.