Some years ago (around 2004) I think Intel showed off a new best of class image uprezing software, that took something like 100 hours to uprez one frame and bring out new detail. With modern GPU processing maybe you could get a reasonable rate. In the late 80's and early 90's, fractal compression was the go, and it could automatically scale the picture and bring out hidden detail (apparently). Also in the mid 2000's Intel showed off 2D to 3D converter software, concepts I had come up with ears beforehand as part of my other research. What they might have figured by now is that combining this 3D conversion with image restoration, gives a very powerful restoration tool.
It is a matter of which methods you are using and how much processing power. You might be unlikely to produce an credible cinema like SHD footage from a sub SD security camera (without artificially filling in details) but there was a company using a farm of powerful servers to restore early century decayed cinema footage to normal quality, in a fashion similar to my previous ideas. Even camcorders these days have caught up and are comparing subsequent frames intelligently to remove unwanted noise. It is just a matter of systematic processes to derive the data.
I only have a meager knowledge of this side field from my main fields. So I imagine there are even better tools out there available to various levels of government agencies, but most of the time on TV it is probably just convenient to use sensational tv rubbish, and most police stations might have access to, or download, common tools over the internet, and departments maybe progressively something better going up the hierarchy.