I have always insured my boats. With the sue happy society we have today not having some sort of liability insurance is risky. All it would take is one small accident with another party to cause you lifelong financial harm.
That said, my insurance has paid for a few damaged outboards over the years. I hit a submerged log once and trashed a lower unit, i hit a submerged dead deer once and tore the lower unit clean off the midsection, hit a sunken ice fishing bobhouse and again tore a lower unit clear off. All of these were in a tournament bass boat going 70mph. Insurance covered them all without question.
i have also have had a similar thing to you where i have picked up plastic bags that people threw out into the water and even one time a poland springs water bottle that have completely blocked my water intakes. I have never had it melt down a motor tho, mainly because i have a water pressure gauge and also a low water pressure alarm that gave me instant warning so i could get it shut down quickly.