@Gustaf9
Small accidental damages are a cost of doing business that you should build into your nightly rental rate and not bother charging for.
Yes, Airbnb “insurance” applies only if the guest declines to pay, and guests do not have their own insurance.
You might or might not succeed in collecting on larger claims from Airbnb. If the guest declines to pay then Airbnb adjudicates and their decisions are known to be quite capricious. On this forum you will find many posts from hosts with very major damage for which Airbnb paid nothing.
You need your own insurance. Do not count on guests or Airbnb to make you whole in the event of a major loss.