Actually, most states allow for alternative evidence of financial responsibility, these sort of things include a cash deposit with the DMV, A DMV issued self-insurance certificate or a surety bond of some type. Why are these not allowed with Obamacare? Because they do not provide them with the cash flow they need to pay for such things as abortions and health care for illegal immigrants.
What you described is a form of liability insurance, only you prove that you are self insured.