It sure would prosper. It's called nuclear weapon parity. A concept which should be pretty obvious in this day and age.
Everyone has access to the codebase of my open-source video NVR system which in turn runs on an open-source Linux distro. And anyone remotely familiar with IT administration would trust open-source software much more than some proprietary NVR running ActiveX, which most of them do. I can come with a million more examples, really.
I have no problems with open-sourced home security. In fact, I'd rather prefer it to be easily auditable and backdoor-free. Something proprietary software is absolutely unable to guarantee.
I don't use fingerprint or facial recognition either. I'd rather keep my personal data to myself.