You should look at this from a legal perspective. Now I understand the "real" situation, and that everybody should just magically know it, and the world should be just and true and ...

Fact is ... it isn't. You don't know if people are playing fair or not, and that means

1) at some point you make a guess if they are ... or not. There are going to be false positives and false negatives.

2) there will be disputes about this

So we need a justice system.

Ok, now let's see how people react once they get into the situation where there's an actual dispute about whether they stole or not. That dispute can happen regardless of whether you stole or not, and either side may be fraudulent, uncooperative, overworked or absent, just to name some basic problems.

a) they never have any real legal knowledge, so they are not capable of playing by the rules of the justice system, even if they want to. Nobody does even an introductory course (even though, you're actually sort of legally required to know all laws)

b) they don't have a lawyer, and they refuse to pay for this. So they don't know the law, nor are they willing to pay for having someone explain the law to them and give them advice about their options.

c) they also don't want to pay taxes to have an extensive police force. So elected officials (presumably with your approval) have instituted "pay per conviction" rules, to measure police force effectiveness.

So what situation is a cop and, later, the assistant prosecutor in ? They have someone who doesn't know the law, won't get someone who knows the law to talk to you, and your boss is shouting at you that you can't explain their options to them you don't have the time, and, oh by the way, if you don't get them convicted it's 50$ less money at the end of the month.

Are you starting to see how this works ?

Now, get a little taste of the US legal system from a criminal justice perspective: https://www.youtube.com/watch?v=d-7o9xYp7eE

At least that video will give you some idea of exactly how a police officer will work, how a defense attorney will react in a very general sense, what the prosecution will do and exactly how people get fucked by the system.

Oh and I forgot the last, sad and stupid, little fact about the legal system

d) it is in the majority of cases impossible for a convicted criminal to actually uphold the judgement (say, paying for a stolen and damaged item). They just don't have the money, nor do they have the inclination to work to repay their debts. That's why the vast majority of criminals are criminals. So the only option is to punish them, no other option is available.

d bis) this means that in the vast majority of cases, reporting a crime to the police gets you ... nothing. If you have a theft, you will only very, very rarely get your goods back even if they find and convict the perpetrator rapidly (which itself is not exactly the norm either). It is actually more common for people to get in legal trouble for reporting a crime than it is for people to get satisfaction.

The TLDR: you CANNOT COUNT ON THE POLICE FOR ANYTHING. Unless it's a violent, personal crime, don't report a crime. You will not get stolen goods back, and it is reported that something like 20-30% of convicted criminals are innocent (at least of what they were convicted for), so what are you trying to achieve ? Get the necessary paper for the insurance if you must, but that's all. Don't attempt to give a description of a perpetrator that you only saw in a moment of pure panic and anger, because it's going to be inaccurate as hell. For the love of God, do NOT report your suspicions (everyone's neighbor was looking funnily in their window the day before the house got robbed, didn't you know ? Especially the neighbors they don't like). And I get that 5 people in your class look at you like they'd like to hurt you, if you then got robbed by a big guy, it wasn't one of them. It especially wasn't the one you like least, and you don't want to ever have any police attention focused on you or anyone you know, even if you don't like them.