I feel compelled to share an experience with one company people have mentioned in this thread. When my dad and step mom were killed in a motorcycle accident, I managed both of their estates. They had Allstate and Progressive between their homes and vehicles.
Progressive Insurance WAS NOT good to deal with in this tragedy. Adjectives that describe them at various stages of the accident, funeral, and estate processes are: callous, incompetent, slow moving, reluctant to help. At EVERY stage of the estate process, Progressive was a nightmare. One example of many I could provide: Progressive literally "lost" our claim paperwork multiple times, at two stages of the process, by three different people. Mind you, this is in a situation involving the death of two people.
Just to be clear, MOST companies I dealt with were amazing, compassionate, and very competent. Some even went way above and beyond anything they needed to. However, there were a select few companies that were just God awful! Progressive Insurance is one of three that was horrible.
For Progressive, I have broken my personal rule of disparaging businesses as we can all have a bad experience with one person that doesn't fairly represent a company as a whole. In this case, Progressive had systemic break downs in an accident claim involving two deaths.
I can appreciate that they often have cheap rates. We considered them a few times over the years prior to this past year and my parents accident/deaths. However, from this personal experience, I would have ZERO confidence in them doing their job appropriately or competently in a claim situation. I would hate for others to have to deal with them in the ways I had to.