For instance, in NYS you cannot waive or remove the personal injury protection part of the coverage.
There is a world outside NYS (and Michigan). In NJ & PA, there are multiple tort options that can save an insured money in exchange for limiting tort rights. In NJ as well, you can buy more or less personal injury protection (PIP). Even in NY, you can add a PIP deductible, and drop optional PIP (which does exist).
But, at least in NYS, the company could only do that prospectively, meaning that they have to give advance notice before the cancellation or non-renewal can go into effect.
See note above. In general, case law does agree, with the exceptions that I mentioned earlier regarding fraud and/or misrepresentation. However, once again, it does not mean that the insurer will not try to deny your claim (and do you really want to go to court?)