Embarrassing is what it is.
I would think that home insurance companies would want to put a stop to this practice asap in order to minimize their losses. They have a powerful lobby, so they should be able to make it happen.
Does a doctor in an emergency room not try to save your life if you're having a heart attack because you didn't pay your health insurance? No, they save your life, then send you the entire bill.
Fire protection should work the same way. Didn't pay your annual due? They should stilll put out the fire, then bill you for the service, say $1000. If it's not paid, it can go on a lien against the property, same as if you didn't pay the property taxes or other assessments. The house couldn't be sold without paying off the lien, so they'd get their money sooner or later.