With a mortgage, if your house broke down you still have to fix it. With a landlord, you're paying their mortgage. It's a service. They fix stuff for you. End of the day you're paying them for a place to stay. If you can stay there, then you don't pay. It makes no sense to demand rent for a service you can't provide.

If they want, they can get insurance to cover the mortgage.

A stupid analogy would be going to a shop to get ice cream, but they ran out of ice cream since it's a hot day. But you still get charged because the shopkeeper still has to pay his mortgage.

Mortgage != rent.