Insurance isn't a magic word.

Insurance works on risk profiles. Insurance also works by limiting exactly what situations they do and do not cover (see: All the people who 'thought' they had flood insurance over the years).

Something tells me insurance is going to be a lot more expensive for BTC, which can have a range of impacts that will make it unpalatable for the average consumer, if they or online services can even get (try insuring a Audi R8 under an 18 year old's name...)