I have no desire for someone to force something on me “for my own good”. If something is truly beneficial, then the public will freely adopt it; people generally won’t willingly endanger themselves. What the conversation should be about is if you are endangering the life of another.
Side note, your argument for throwing ice on stairs is lacking scope. If it was one’s personal stairs then by all means; however, an area that is to be expected to be used by the public cannot willfully endanger them; If not a criminal charge, then it is certainly a lawsuit waiting to happen. As for removing car brakes, again that depends on exactly what you mean. If the car is not in such a state that would recklessly endanger the life of another, then why would it matter?
All in all, one should look at things in such a way as to balance public safety, and individual liberty. It is always a trade off. I personally would err on the side of liberty, but this is not without its realistic restrictions.