Would you mind explaining what the perverse incentive is here? If I want to insure a pillow that I claim is worth $1 million, why should it matter what others are willing to pay for it?
Even in the legit cases the insurance companies have to account for the "don't worry, it's insured" mindset. Keeping the ceiling on the insurance value is intended to leave at least some of the incentive to prevent the damage with the owner.
The insurance companies cannot rely solely on the "don't be careless" contract clause.
So what, though? Can't they just adjust the premium to account for that? It's not like they can't do their own modeling of what the item is likely worth -- if they see it's 1% of what you stated, then they can just as well cite you a ridiculous premium so that you wouldn't feel it's worth it. What's wrong with that?
It makes the market for insurance much better if everyone actually has insurance. Because it reduces cost. It also keeps the industry legitimate, preventing gambling legislation from applying, and anti-gambling activists from targeting insurers.
You'll have to go to a bookie if you want to gamble.
I don't get the comparison to gambling either, that reads more like an appeal to emotion than actual reasoning.
This doesn't pass the smell test, though. The premium would take care of that. You've told them you have a pillow, and that you want it insured for $1M. They could easily look at it and go "hm, this is worth $10", and give you a absurd premium of $999,900 in exchange for your absurd valuation. So happy accidents won't be worth it anymore. What's wrong with just letting the premium take care of it?
Because the actual value of the item determines your incentive to commit fraud.
If you insure a $10 pillow for $10, when you damage your pillow, you personally will definitely be out $10's value in goods in the hope you'll recover that $10 later. Since your only outcome is mildly negative, you don't have any incentive to file a false claim.
If you insure your $10 pillow for $1 million, as soon as the insurance is in hand, will have a strong incentive to destroy the pillow and try to collect a million dollars, since $1 million - $10 = $999,990.
This incentive exists regardless of what premium you had paid for the insurance (since it was a prior cost), and can't really be perfectly mitigated. Yes, you can criminalize fraud, ask for evidence, etc. but courts aren't perfect and it's always possible to be clever and fool people.
Also, some people are honest, and others are dishonest. An insurance company can't perfectly tell ahead of time who is who. Let's say I quote you $500k premium to insure your pillow for $1mm. A fraudster will see this as an opportunity to profit by $500k - $10. An honest person would see this as a terrible deal. Therefore only fraudsters would take this deal. If you continue to work backwards, as an insurance company you know there's no premium that you could quote that would end up in honest people taking this deal—there's no stable equilibrium where the premium charged ends up outweighing the (potentially fraudulent) claims.
Btw, this situation is famously described in George Akerlof's paper The Market for Lemons (he called it "market collapse"):
https://en.wikipedia.org/wiki/The_Market_for_Lemons#Conditio...
Another way to see this: rationally as an insurance company, if you ask me for a policy for $1mm on a pillow, due to the risk of fraud I will likely be quoting you close to $1mm as the premium. You (as an honest person) rationally would never take this policy. Therefore, I shouldn't even bother offering it, to save everyone involved time and energy.
I would love a clause in the contract where for non-rare goods you have the option to have the insurance company make you whole by buying you a same model, same trim or higher, same miles or lower, same year or newer car. Like you claimed the market price was less then half of what I can buy it for, use whatever contacts you clearly have and buy it for that.