It seems you could safely drop auto insurance from what you posted. However, if you are the driver, even in a rental and you hit someone and are found to be at fault, it will cost you a fortune. You can be sued and wages garnished and tax refunds held to pay your obligations. I know people this has happened to.
If you live in a place that requires you to carry car insurance and you are caught driving without it, it will cost you a small fortune and years of headache to fix it.
I would find other ways to save $$$ and keep myself insured. In my province (canada) we require auto insurance by law. When you do not have insurance the companies will rate you low and a liability. But when I was not driving my insurance company said to just put fire and theft on the vehicle (even if I did not own it) they listed it as a stored vehicle and it only costs me $21 a month but more importantly I did not loose my good standing.
Also apt insurance is a must but get only tenant insure which covers your belongings but not the building. The building is the landlord’s responsibility.