We're comparing a short term ban on provable lies about a cheap, safe and highly effective set of vaccines with a long term, permanent ban on all activities that could increase the risk of heart disease of cancer.
First, vaccines highly effective. Even if the draconian measures you proposed were implemented, would they even reduce the heart disease and cancer death totals? How much would the reduction be?
Second, vaccines are not an egregious imposition on your lifestyle. The cost is tiny, the time taken is tiny, the side effects are minor. I can't think of a single significant change in my life due to having been vaccinated, other than not worrying about dying due to Covid.
Finally, the ban on misinformation would be temporary, because the crisis will pass. Like wars, pandemics are temporary. Even before vaccination and modern medicine was invented, pandemics eventually end. When would the draconian measures you're proposing end? Heart disease and cancer are not communicable diseases. Your solution isn't a sustainable long term answer to anything.
Your comparison is frankly very dishonest and disingenuous. Wanting to reduce provably false misinformation about vaccines is nothing like the draconian, permanent measures you're proposing.