Seems to me

you are totally an insurance lind. Can not image you live in the US.

The insurance on your car is the so called liability insurance, it is only covers the other car and this is required by law. I am prtty sure the term of this insurance was stated on the insurance contract you have signed. If you do not understand it, it is your problem, you can not blame others. Liability insurance is much cheaper than the full coverage insurance, you have enjoyed the benifit.

In case of accident that you have no fault, the other cars insurance will cover your loss, you need to contact the other cars' insurance to get your car repaired.

This is a quite fair play, no reap off what's so ever: You pay less for less coverage.

You have to understand the thing before you sign, contract is leagal banding there is no regreat for signed contract.