FOIA allows for "reasonable costs." For example requesting a copy of Obama's birth certificate is something like $20.
There's a real problem though- anybody (might need to be a US citizen) can FOIA any document anywhere in the US that's not excluded. When they can punt you to the paywall and then reply with a generic reply to a birth cert it's one thing.
When you have to actually find people to do the work of reviewing ALL video footage as $small_fraction of 200million people request every second of recorded footage from every camera... You're(as a city) kinda screwed. If they claim privacy they have to be able to prove it but can charge slightly more. But, if they don't then they have to provide the specific request (possibly a little more- say 1hr segments) at a cost representative of the labor involved... Which doesn't include the cost of trying to staff a FOIA center larger than your city.