No big deal is it was just video. It's really about the data that can be extracted from the video such as who you meet, when you are home or not and who is at your house, etc. all in realtime.
Yes that should all require a court warrant based on probable cause.
Because that will never be abused.
I hope sarcasm is working well for you. To clarify: it would be abused without systems, therefore add court warrants to access any personal information. Criminals are already abusing society by knowing that most of their crime will never be caught.
Is there evidence these systems reduce crime?
There is evidence that systems reduce crime, yes. A system is probably the only thing which has ever meaningfully reduced crime. A law. A strategy. A process. I think you're meaning digital systems though. I'd say digital systems are part of every system now.