It's not "gotcha", just... there are many clones of Android that work without Google Play, because Android (AOSP) is based on Linux. Why not just use that? What does "linux phone" add?
People want a "Linux Phone" but have trouble explaining what software stack they want and how Android is not already it.
People mocked Stallman for saying GNU/Linux. Turns out it's important to specify what you're talking about, or people will misunderstand you. I use Debian. If Debian rebased to BSD (forked and relicensed to GPL, with gnutils) I'd probably still use Debian. If iOS rebased to Linux, I still would never consider touching it.
My opinion is that people actually want the political protection offered by the GPL and the people and projects who stick to it, like Debian (and others.) They do not acknowledge this to themselves. They usually want to be able to layer a few proprietary toys on top, but those are visitors who will be ejected for bad behavior, and they want an OS that will rat on that bad behavior when it sees it. They are afraid of this political project because they are afraid of politics (or because their professed meatspace politics turn out to be the opposite of what they actually want in their own lives.)
https://github.com/microg/GmsCore, so basically you cannot. It's monopoly in daylight.