The only times I ever remember seeing a dentist or doctor as a child was at school. I'm quite healthy physically and I'm very grateful for all the care I got from the various professionals who cared about my well-being and development more than my actual parents did.
We had free healthcare including dental, mind you, my parents just couldn't be bothered. When my brother, as a teenager, asked our mother if she could take him to his orthodontist appointments (which he'd already arranged for on his own) she basically told him she didn't feel like it and he had to take the bus.
If I could improve anything about that system, I'd take it even further and make it so kids could see a doctor and get meds, treatments, therapy, tests, disability aids etc. without having to rely on their parents as well. I shouldn't have had to put up with being bullied and guilt-tripped about the family finances and the time investment needed to take me to the optometrist every time I needed new glasses.