No I don't think so. Why should they? And how on earth would you enforce it?
The point of car insurance is to make sure you can cover any costs incurred in an accident, which can be a lot with a car accident. I can't imagine that a bike accident could create the same kinds of costs. Insurance doesn't prevent accidents or make people better drivers.... so if you are concerned about cyclists in the city, perhaps what they need is better training rather than insurance.