Lyft for example brands themselves as a "friends giving friends" rides type of arrangement and they call the money exchanged a "donation" so they tell drivers, "who is your insurance company to say you can't do that"!

Uber acts like personal insurance will cover it as well if you are an UberX driver but then in the fine print it says it is the drivers responsibility to confirm driving for a "P2P" ride service is ok with their insurance company. Of course if you call any of the major insurance carriers and ask them they will tell you, "hell no that isn't covered".

If you look at the taxi insurance market it is made up of a bunch of dinky little companies no one has ever heard of or in some cases taxi's are insured by quasi government insurers of last resort or by verifying you have the minimum insurance requirement on hand in cash. None of these options is cheap so it isn't surprising that ride sharing services would want to avoid them because they would have to end up paying the drivers a lot more and they would no longer be 30% cheaper than taxi's