Android is pretty easy, you just add it to the keystore and that's it. I've had my own CA long before Let's Encrypt, but now mostly only use it for non-public devices that can't easily use Let's Encrypt (printers, switches, etc).
Doesn't need a custom ROM, but it's so goddamn annoying that you might as well not bother. I know how to do these things; most users won't and given the direction the big G is heading in with device freedom, it's not looking all that bright for this approach either.