It's going to depend hugely on the jurisdiction, as attitudes to policing and the use of force vary enormously between countries/cultures (and even within them). This influences how policing is done within a country (values / priorities / methods), and how it's perceived – and of course how other cultures' policing is perceived.
For example, some cultures like the UK have a very low level tolerance of police violence, and police are expected to resolve things without force wherever possible.
In the UK, any officer using lethal force is (I believe) automatically suspended pending an independent investigation. We're very keen on "watching the watchmen", and ensuring that the police do not make routine use of lethal force.
So in the UK, someone with super-powers using lethal force will be looked on especially poorly – and it's not unlikely that they'd be proactively kept away from anti-terror raids and the like, just to prevent the minefield that'd ensue should they kill someone. Or they might be used as a meat-shield but not allowed to hit people. This might of course provide some good tension for a story – "I have this awesome power, why can't I use it?"
In the UK, the police instead rely on massive surveillance to make catching people easier. A very high proportion of court cases are decided on the basis of CCTV footage. We (largely) don't care about the level of surveillance, though other cultures would see it as a massive issue.
It's quite possible that super-powers would be particularly useful in non-lethal scenarios – catching suicide attempts, searching riverbeds, etc.
In the US, where police use of force (and lethal force in particular) is more common, a super-strength policeman would likely be highly popular. A culture which has people with superpowers would quite possibly be far more extreme in this direction. From a US perspective, this trait of using lethal force is largely not seen negatively, but as an important part of a 'strong' police or similar – whereas from (even a right-wing) UK perspective, the rate of police shootings in the US is extremely concerning. This type of contrast of values would again provide interesting tension for a story – cf. Marvel's Civil War arc.
So the simple answer is that it'll depend entirely on the culture of the society / police force. Imagine a similar issue – police force is offered indestructible, super-fast cars.
- In the US, they'd be deployed continuously, as (I believe) the US priority in a car chase is to resolve the chase as quickly as possible, typically (if TV be believed) by pursuit with a large number of vehicles, and the use of force (often lethal) to end the chase.
- In the UK, they'd sit idle, as the UK priority is to reduce the number of injuries/fatalities – UK police have previously been criticised when a perp has crashed while being chased even if no-one other than the perp was injured. So the UK response to a car chase is to leave them alone (largely preventing accidents), and put up a heli (can't be outrun by most cars, but doesn't put psychological pressure on the perp to drive fast/dangerously), and then catch them safely when they stop or give up.
Your original question mentions super-strength; from a UK perspective, super-strength would be of little value, but powers relating to e.g. vision or flight might be highly valued. So the types of super-power valued in policing in different cultures would vary.