This is exactly my experience with insuring my own aircraft (a 1979 Beech Sundowner 180). Although the market for GA aircraft has tanked in my part of the world and the Agreed Value has declined.
The caveat here is that the insurance company will balk if you ask to insure for an Agreed Value greatly above the true market value of the aircraft. They don't want to pay out for much greater than true market value (at my end of the scale the premium difference on a $10k delta in agreed value is fairly small). And of course I don't want to pay excessive premiums, so it's in both of our best interests to assess a fair Agreed Value.
Slightly off topic because this likely does not apply to airlines (possibly excepting Qantas
):
The other factor for GA aircraft is that you really do not want to overinsure your aircraft. The insurance company decides on write-off vs repair based on a certain percentage of the insured value. If you overinsure, they could decide to repair a plane that should have been written off. You are left owning a plane worth much less than it was previously because of the damage history. Some insurance policies have a "value correction" clause to avoid this situation.