The insurance doesn't cover repair costs, it covers the financial damage incurred.

If you bump somone's car destroying its blinker, and repairing the blinker would cost more than the car is worth, then the insurance will pay out the value of the car only because that's the maximum financial damage the owner can incur. Of course, usually, the insurance will pay the repair cost. However whether you get the repair actually done is your decision alone, as is the consequences of that. You may opt for cosmetic repair, or none at all, the payout doesn't change.

Likewise the garage door. OP is talking about the useful life of the door whereas the insurance pays its book value only as this is its residual value. Unfortunately it's (probably) older than 20 years so its book value is zero, thus no pay by the insurance because financially speaking there's no damage.

Case in point:
A neighbor hit my car while it was parked in front of my garage. Estimated repair cost 2k, that's what I demanded from the neighbor. However I don't really care about the dent so I only had the garage paint over the most obvious stuff, quick-and-dirty style, and kept the difference. The resale value will be lowered accordingly should I decide to sell it forward, that's the damage and what I got reimbursed for.

I guess this is the point and where the "amorisation tables" have only limited scope. If, for example, a hand worker caused the destruction of Thun castle, say by an accident with a blow lamp, his insurance company could not argue there was no financial liability because it was built around 1200 AD and was, therefore, amortised.

Moot point, the handwork would not have enough 3rd party cover to pay the claim. Exactly this happened at the Grands Montets Top lift in Argentiere Chamonix a couple of years ago. https://www.planetmountain.com/en/ne...cable-car.html