And you could set up society so that you'd be useless without carrying your phone, as we're most of the way there already. Not streaming your complete data to the government would become a crime.
All public places could be recorded in a similar way.
If you combined it with satellite tracking of the whole planet, you could even identify people that have chosen to go off the grid for some period of time, so you could solve crimes that happened in the forest if you want.
That's pretty close to perfect surveillance.
I can't think of a crime that couldn't be solved this way, but it's not a society where I'd want to live.
I'm not sure why I'm being so heavily downvoted, the only difference between the dystopian future that I describe and the system we have currently, is that the government isn't collecting and processing data on such a wide scale. If they collect more data, we will have more crimes solved and more privacy forfeited. If you take that to its logical extreme, we have full surveillance, no privacy, and no crime. I'd rather live in a world where we have some crime, but privacy and no surveillance, but I think it's far more likely we'll head in the opposite direction.
Unless the state itself is criminal. Not only can law stray from morality, authorities of the state can even violate the laws of that state itself. If you can imagine an extreme authoritarian state with a constitution, can't you also imagine that the leaders of that state choosing to ignore that constitution?
But before even getting into the above, you've assumed the possibility of perfect surveillance. Who or what and how could that ever be possible?
The only way I can conceive of perfect law enforcement is to have very few if any laws. Everything else is an excuse for the personal fancies of authoritarians.