I haven't been sick in 12 years. Yet, every year, I pay taxes to keep the public healthcare system running. Even though it's not something I use, undoubtedly, there are people who need it, and wouldn't be able to pay for it if it wasn't public.
About a month ago, I exhibited the symptoms of some kind of ventricular tachycardia (heart arrhythmia). As advised by a friend in medicine (in a different city), I tried to get myself booked for an ECG, to see what exactly was wrong. Without getting into the details, let's just say that even to this day, I haven't been able to get one.
I can definitely see why people don't want to pay, not just for services that they'll never use, but for services they'll probably be unable to use, even if they ever need to.