I am not saying it's ok but you post sounded as if TK is the only leaving people's bags everywhere.
The whole point of a proper travel insurance is to have zero excess. At least in Denmark, Sweden and the UK I know my travel insurances are always with zero excess.
My bag was "lost" for 20 days and on exactly the 21st day it magically appeared because Eurowings doesn't want to pay for the lost bag. That's why EW is my no go airline.
When I tried to claim with my travel insurance what it requires is a statement from the airline that they won't pay.