Yes - British people are too keen to assume that all US habits are about money when the UK is the outlier. Preventative visits are actually a financial loss for doctors, and the US isn't unique in doing them. Same with direct access to gynaecology. Having had small children in both I prefer the American system and think it picks up on developmental delays and other issues more quickly. Preventative visits are actually pushed by the system in the theory that chronic conditions will be picked up before they become serious and hence be better treated. I have Type 2 diabetes and it was picked up before I had obvious symptoms.
The US system allows family practitioners (FPs), paediatricians, and internists do primary care (there's also advanced-practice nurses and PAs, but we'll stick to doctors here). Family practice is similar to UK GP training, including OB/GYN rotations, and they're particularly common in more rural areas. After an internal medicine or paediatrics residency, a doctor can go straight to either primary care OR to hospital practice. Or they can continue to subspecialty training such as endocrinology or cardiology. There's also med/paeds which allows a doctor to specialise in either following residency.
American midwives are nurse-midwives who do a master's programme following their nursing degree, and can do primary care, antenatal care, and deliveries. I see one for my well-woman care. (I had high risk pregnancies and saw an obstetrician, but I was also consultant-led on the NHS.)
My children have a regular pediatrician they see for well visits, vaccinations, and if they get ill. But the two with autism also see a developmental paediatrician at the children's hospital.
It also depends on your insurance if they require a referral from your PCP to see a specialist, and some specialists have policies requiring a referral.