Many alternative AOSP-based systems work fine today and do not have the new Android Developer Verifier (wow, already rolled out to 500M+ devices [1], though still dormant).
To be honest, it is quite scary that Google is able to remotely roll out an app like that to all GMS Android phones. Of course, we all knew that, but it highlights again that Google can remotely take away functionality that you had before, brick your phone, etc.
[1] https://play.google.com/store/apps/details?id=com.google.and...
Wait till you hear that your OEM can remotely rollout full OS updates with full access to all your data and drivers... carrying Google software and most of it Google code.
We used to call programs like this, that allow someone to remotely break your system, a Trojan horse...