One question I have is, what happens when you have no car insurance and you're hit on a bicycle?
The person who is at fault is supposed to pay, whether they hit you in your car, on your bike, or on foot.
No one suggests that pedestrians should have auto insurance in case they get hit by a car.
Of course, you have to make sure you actually aren't the one at fault! Ride legally and safely - on the correct side of the road, stopping at stop lights and signs, using lights at night - and its a safe bet that if you get hit, it was the drivers fault.
Even if you
were at fault though, there is very little damage you can do to a car while on a bike, so you wouldn't need to pay much anyway.
And even if they are uninsured, your biggest risk is medical bills, which should be covered by your health insurance.
All that said, when me and my ex-wife were living in New Jersey, she was hit by a van on her bike ride to work. The other driver had a stop sign, she didn't, but the driver said he expected her to stop!
Turns out NJ has some stupid law called "no-fault" where ones' own insurance in any accident is expected to pay. The other driver's insurance (Progressive) tried to say that because of that law, they shouldn't pay for the medical bills and bicycle damages caused by their driver. The dollar amount we were seeking was too small for a lawyer, but a certified letters to Progressive supervisors, with CC to the BBB, and the state insurance commissioner, eventually got her a check for the full amount.