YABU
Pediatricians are great and you'd see the benefits if you'd ever experienced the same kind of system.
There's continuity of care, regular and frequent checkups from a doctor specialised in children who is aware of the child medical history. You can pick the one you like and they're available on the phone or by email for advice during illnesses and for medical advice. I have nieces and nephews in my home country and there's a huge difference in everything involving medical check-ups/issues.
HVs are great, but they're not doctors. It's rare to see the same one more than once and they just tick boxes, fill in a chart and that's it. They give weaning and sleep advice too, and so do GPs. GPs are not specialised in children, our old GP for example seemed to not have much knowledge of certain things relating to children, in the end we had to change practice after several issues/mistakes.
Pediatricians check everything regularly and are therefore better equipped at spotting any issues early. Here in the UK the health checks are not as frequent and not even half as thorough.
Pediatricians check heart, eyes, breathing height, weight, assess behaviour and many other things (eg hips, testicles in boys etc) these are really thorough check ups. They're monthly as babies and then they get more spaced as children grow older becoming yearly for older children until they are 14.
So nothing weird about pediatricians, they're a wonderful thing when available. And in my EU home country that's all for free, so it's not all about money as some people tend to think.