As others have mentioned, insurance companies aren't dumb, they typically won't over insure an aircraft. Does it happen? Sure, now and then, but typically no. In the airline world polices have deductibles just like your homeowners, or your Cessna 172 policy and they usually are between $1,000,000 and $500,000 dollars depending on model, body type, etc.
Geosync you might be surprised that both of the above assertions are not universally true for aviation insurance.
First, since aviation insurance uses "agreed value", it's very common for insurance companies to de facto "over insure" an aircraft. And they don't really care, since the insured is paying enough premium to cover the "agreed value". In other words, over insurance hurts
the aircraft owner, not the insurance company. It's up to the aircraft owner to periodically get a new appraisal and reduce the "agreed value" if necessary.
The insurance company sure wont complain collecting higher premiums!
YRP also brings up a very important point above. If the aircraft is "over insured", then the insurance company may elect to
repair a substantially damaged aircraft instead of simply writing it off and paying out the full agreed value. This can be highly detrimental to the aircraft owner.
In the airline industry this becomes important because, as you know, a large percentage of airliners are leased. (E.g., I believe the accident Air Canada aircraft was leased).
In a dry lease arrangement, the lessee is typically required to insure the aircraft with an "agreed value"
not exceeding the aircraft's replacement value, to prevent over insurance. Otherwise, in case of an accident the lessor (owner) might get stuck with a "repaired" aircraft with a substantial damage history and severely diminished value. Again, this restriction to prevent over insurance is from the aircraft's owner, not from the insurance company.
Regarding deductibles, many aircraft insurance these days are written with ZERO deductibles. Remember that deductibles were designed for things like car insurance where there tends to be frequent but relatively small claims -- fender benders, cracked windshields, dings on doors, etc. Aircraft insurance is the exact opposite: there's rarely have a claim, but when there is one it's usually
catastrophic.
So compared with car insurance, deductibles play a smaller role in aviation insurance. Sometimes there is a fixed deductible and the insurance company will not give an option of a higher deductible in exchange for a reduced premium. And if there is a deductible, the deductible has to be very high (over 10% of the agreed value) to make the premium reduction worth the extra risk.