I'm sorry but this is hoplessly naive. It's Chicago. One of the most historically corrupt machine governments in the USA. Nothing gets done without dozens of people getting paid off if not in cash than in favors or quid pro quo. It's not even something that people on the inside find unusual. It's just how it is, and always has been.
It's a much bigger problem than just mandating tamper-proof cameras.
This is why I state, these items must be tamper proof and back by regulations and laws. Likely all this must be at the federal level and it become a crime on the federal level to tamper with them.
So you make it nearly impossible to break/tamper without trying and its a federal offense to do so. Simple.
Who is buying the cameras? Who is installing the cameras? Who is determining if they are tampered with? Who is making the laws concerning the cameras? Chicago city politicians or employees. All of whom are being paid and influenced to do do their jobs in a way that favors the right people.
You seem to be suggesting a federal takeover of the Chicago police department -- a city whose mayor is the former chief of staff of the president, who himself is a Chicagoan. Good luck with that.
It's a much bigger problem than just mandating tamper-proof cameras.