I really did not want to enter this fray, but some 
of what you said is inaccurate.

The example you gave of the car is instances where 
the damage is repairable and the cost to repair 
is less than the cost to replace. In this case, 
insurance will pay the lesser amount (the amount 
to repair the car and you keep the car), rather 
than the amount to replace the car. If 
they paid you replacement cost of vehicle, the 
insurance company keep the car and get the title.
This has happened before in our family.

In regards to claims at the post office, what you 
are filing is a replacement claim, not a repair 
claim. For this reason, you give up all rights to 
the property if the post office accepts 
your request for them to pay the replacement cost 
of the item. Unfortunately, you do not get to bake 
your cake and eat it to.

However, if you go to the surpervisor level or 
above, you can often re-purchase the damaged good 
from them for a cost that is less than initial 
value. Usually an offer of 25% of the listed value 
is usually accepted. This practice is not usually 
doable at the level of postal workers, but let 
them know that you are going to try this and so 
that they put the item in a safe location.

In some cases where it is very obvious that the 
item is completely destroyed, they may not ask for 
it and just note it on the form.  However, as of 
the last time I read through their insurance claim 
process, they are required to keep the item if a 
claim is accepted along with the packaging 
material.

Marcus