As others have said, every system has gaps, where it is impractical, illegal or impossible to surveil all activity in all points of location and time. It's really not difficult to very easily and inexpensively exploit the weaknesses of even the most expensive camera systems.
One of the big ones for cameras is adoption of a sufficient level of video technology that identifying you using the video feed is even possible. You ever see those grainy surveillance videos of convenience store or retail robbery-shootings, where someone's dead or in the hospital fighting for their life, and the police are asking for anyone with information? You look at the hopeless blob of digitally-zoomed pixels and go "how on earth could anyone possibly identify that guy from that picture?".
Well, that's the point; if the police had a clear, high-resolution still of the guy's face, they wouldn't need the public's help identifying the guy. Despite the proliferation of cheap surveillance cameras, that's exactly what they are, cheap; most of the systems in convenience stores are ridiculously outdated, primitive and of hopelessly poor optical quality, even if they were only installed a few years back. They were sold to C-store owners and managers running their shops on an extremely tight budget, by unscrupulous vendors unloading old, cheap cameras at ridiculous markup. Coupled with non-ideal placement, like up in a corner where they hope you don't notice instead of looking right over the cashier's shoulder from two or three angles (which is more expensive and less discreet), it's little wonder the best the system can do is a 10x10-pixel blob of an out-of-focus face extending their arm at the cashier.
You're handwaving that away by having the government come in and install the very best available technology, but even a country like China, that's spent billions on video surveillance to date, doesn't have the very best cameras everywhere. A criminal can exploit gaps in coverage of the very latest cameras that have the ability to see under facemasks (whatever Applied Phlebotinum you want to use to enable that) by picking his route to and from the target area. If he's one of a thousand people walking down a particular block with a mask on (very common in dense Asian cities, even without an ongoing coronavirus epidemic), nothing will seem out of the ordinary, and even if he's spotted on camera committing a crime, facial recognition may not catch him because he never got close enough to a camera with sufficient resolution and imaging tech to identify him behind a surgical mask.
Your handwave of a comprehensive, overlapping network of cameras instantly accessible to the police from anywhere is a very significant one when talking about an individual's actions or those of any organized team; no matter how well a team does its job defacing cameras, if you have enough, the criminal will spend enough time trying to black out the area that he won't actually be able to commit the crime he was trying to commit before the police show up to stop him.
However, that leads to a much more effective attack vector. Don't take out the cameras, take out the network connections to the recorders and police surveillance centers. Communications networks are inherently tree-based; large trunks feed smaller branches that service the "leaves" of the network. It's inefficient to provide an individual and separately routed dedicated link from each camera to the surveillance hub/recorder, so instead, the signals from a group of cameras are consolidated onto a single higher-bandwidth link. Those links are far more vulnerable than too many people actively realize, and with much more focused application of destruction, you can take out much larger sections of the grid for much longer than throwing a few rocks at camera lenses.
You don't remove a tree from your yard by plucking every leaf; you take down a tree by lopping off branches and sections of the trunk one at a time until there's nothing left. You might be taking out the public internet as well; so be it, if the communications companies are in kahoots with the government to such a degree that the government can piggyback its camera system on commercial internet, then the internet companies can share in the pain. Generally speaking, even in the modern age, the government needs advanced communication technology to work against a resistance more than the resistance needs it to work against the government.
And, if you just want to take out the cameras for 15 minutes so your buddies can hit the jewelry store in the center of the grid serviced by the fiber bundle you just ran a chainsaw through, that's far more effective than defacing or shooting out every camera that could catch the other team in the act. Will you get caught on camera in some incriminating way before you can disable them? Probably. But your buddies are much less likely to, and your share of the money from the heist is more than enough to put your little brother through law school.
Another major gap is that with a camera system, you're looking for visible evidence of the commission of a crime. There are quite a few crimes that have no visual cues. For instance, you can steal someone's identity with an RFID reader in a handbag in relatively close proximity to their wallet. Luckily for real-world society, this fact became pointedly obvious soon after the introduction of RFID-enabled no-swipe cards, and most of the world has instead transitioned to smart chip technology that requires the card to be in physical electrically-continuous contact with the reader. However, the concept of a payment method that is totally automatic and doesn't require you to fish through pockets or set up your smartphone for communication with the card reader is still of very high interest to payment processors, and when they come up with one, there will be a plausible way to hack it.
Want to get darker? You can commit mass murder without anyone having a clue for weeks. Just walk down any densely-packed sidewalk with a backpack. Nobody will have any idea they're already dead for days, even weeks, until everyone that was walking down that block at that time starts slurring their speech, losing their coordination, balance and their memory, and exhibiting other symptoms of wide-ranging central nervous system dementia. A few simple tests will reveal the patient has about 20 times the lethal dose of mercury in their cerebrospinal fluid, and are far beyond any hope of treatment. Death will be a slow degradation over a period of several more weeks, where victims forget how to speak, who their friends and family are, how to eat and drink, how to avoid wetting or soiling themselves, until eventually the toxin impairs the brain stem sufficiently to cause loss of autonomic nerve function and the heart stops.
Because your backpack was spraying an invisible mist of dimethylmercury, one of the most hideous toxins ever devised by modern science, and easy enough to prepare in a run-down apartment with the contents of an old HVAC thermostat, some tincture of iodine, denatured alcohol, a couple road flares and a homemade glovebox. Sure, you're practically guaranteed to be the first fatality, and will suffer all the above symptoms totally alone in your off-the-grid hideaway to avoid being identified as patient zero, assuming you don't put a bullet in your own brain once you get off the grid, bfore the mercury can eat it alive. If you know enough about this compound to avoid that fate, you'll be in very rare company (one of maybe a few thousand people in the country with graduate-level education in organometallic chemistry) and thus probably known to the government as someone who could pull this attack off. So, once you're seen on a busy sidewalk in a business district of a major city you've never visited in your life, police won't need a whole lot of video surveillance tech to connect these dots. But if you want to prove, in the most undeniable way, that the country's surveillance system is worthless to protect people from those who wish harm on them, this is how you'd do it.
That's assuming you even care about not immediately getting caught. Drama writers like trying to write about perfect murders (or nearly so), because they're so difficult to manage and make the writer and the reader have to really think. In the real world, criminals, especially murderers, don't tend to plan too much. If you want a bunch of people dead, you don't worry too much about the perfect murder; you get in a cargo van and mow down a hundred people on a city sidewalk in five minutes.
Sure, your chances of getting away even from the immediate crime scene are basically zero. That's not the point. The point is, 50 people are dead, you did it, and the government, with its all-seeing surveillance system, was totally powerless to stop you, because you did absolutely nothing to tip them off to imminent criminal activity until the second you yanked the wheel to the side and floored it. Just as it will be totally powerless to stop the next guy, and the one after that, no matter how many rights it takes away in the name of public safety. More than a few mass killings, regardless of weapon, have been perpetrated in recent years for the specific purpose of sending the message that no-one, least of all the government, can guarantee your safety, and the pain will continue long after any one perpetrator is caught or killed. That's a message that is only magnified by the multi-angle views of the killings available to the media through the very camera network set up ostensibly to make society safer.
