I don't see them disallowing side-loading soon but what I do expect is an expansion of the
SafetyNet [1] test which will flag devices with
any side-loaded software as 'suspicious', upon which banking and electronic ID apps will refuse to run. Since this will render the device all but useless for many people it will either force them to carry two devices - one for such 'official' stuff, the other for the rest - or to try to find a way around SafetyNet. This is a cat-and-mouse game which has been going on for a number of years and will continue to do so until either Google goes full Apple by locking down the platform or some sort of 'safe enclave' is created which can run on any device no matter its status. Google clamping down too hard will give extra impetus to the further development of alternative mobile operating systems, the viability of which increases with the rise of web-based alternatives for native apps.
[1] https://www.xda-developers.com/safetynet-hardware-attestatio...