I agree that it's efficiency that's the issue.
I had my first baby in Canada (single payer system) - I didn't outlay a penny for anything (except blood tests- but it wasn't a lot) - I went to a midwife practice for my care, I went to an office to have blood tested (there were plenty dotted around the city), I went to the hospital for ultrasounds - ie. quite similar to the UK, BUT they'd thought things through - for example, I'd get a little card to come to a community centre for my baby's jabs - I'd join the queue, he'd be weighed measured, they'd have a chat to see that all was OK while they did that, then we'd go to the next room for jabs, and head home. 6 people, servicing a room full of mothers and babies for a day - and I just had 30mins taken to get it all done.
In the UK, I had to go to one (roving - I never had an appointment in the same place twice!) clinic for checkups, another for jabs at my local doctor, and there was a 3rd where I could go to have my child weighed if I wanted, and yet another HV to check I was doing OK. - More people, more resourses, more time wasted, for no better effect.
I was chatting with the nurse who gave me my smear about it - and she agreed - in fact, she'd switched to the practice nurse from HVing because it frustrated her so much how ridiculous all the innefficiency was.