It takes way more investment to do what you're asking. Collecting the video, getting a warrant, tracking down the person, sending a team to arrest them, etc. How much does that all cost the city? Average cop makes over $50/hr in San Francisco. So it probably costs more than the loss typically?[1]
The problem in SF is that we've disbanded the team that tries to catch people in the act[2]. IIUC, it's both because there weren't enough resources and the DA won't prosecute anyway, so what's the point.
Sure if each criminal act was done by a different person, it probably would be expensive. In most cities, very small set of people are responsible for 99% of the crime. So if you book a single person, it will prevent multiple such incidents and bring down the cost and will be worthwhile. It's not a cost problem, it is a politics problem.
Besides doesn't matter how small the crime is. If tomorrow, if what the DA and the cops are are doing get written into law, ie, anything that is of less value than what costs us to prosecute is legal, the society will descend into chaos very quickly. Like why the hell am I paying for groceries?
Again, it's a service paid for by citizens taxes. It shouldn't matter they don't make enough money covering the "protect and serve" part of a non violent crime, that's the damn job. Raise the taxes, don't skip out on the duty you're paid to do.
The problem in SF is that we've disbanded the team that tries to catch people in the act[2]. IIUC, it's both because there weren't enough resources and the DA won't prosecute anyway, so what's the point.
[1] - Maybe not in the case of a-rod: https://www.sfchronicle.com/crime/article/Half-million-in-lo...
[2] - https://www.sfweekly.com/news/authorities-hustle-to-curb-s-f...