No, we do not have a door bell camera. We have considered cameras, our alarm company offers a 4 camera system for a $150 installation fee if you sign up for 3 years monitoring. Our daughter had a 4 camera system on the house she just sold, She monitored all the cats walking through her yard, knew when the trash was picked up and mail delivered, but never caught any crime in five years. She did have an awkward situation where one neighbor suspected another neighbor had backed into their car on the street and they asked her to check her cameras. She did, and fortunately it was out of range of her cameras as she did not want to be in the middle of a dispute between neighbors.
I guess it would be nice to see, but from a crime perspective, all I can say is our Neighborhood Watch Facebook page and Next Door are full of videos of crimes being committed and they never seem to deter the crime or lead to an arrest. Porch pirates just don't care if they are recorded because they know in California, if the item stolen is worth less than $950 they won't be arrested or prosecuted.
Actually, the big thing right now on both websites is illegal dumping. One business is always posting videos of stuff being dumped behind their building, but it never stops it, and never results in an arrest. And there is one person who is a chronic illegal dumper across our community, his truck has been clearly recorded many times over the last year, someone staked out the location and recorded him with their cell phone. Got his face full screen, guy doesn't care, nobody has been able to identify him, and he just keeps doing it.