This is very common in my home district (regional SA), there are 2 regional public hospitals 2-3 each hours away but I would say a high percentage (75% or more??) of my family and friends travel the 6-8 hours trip to Adelaide for either public or private hospitals. So many women are doing the whole weeks away from home, extra expense, being away from family (including older siblings), friends and support networks, then travelling long distances home.
The regional hospitals only take from 36 weeks so many women get airlifted as soon as they get a contraction before 36 weeks. The regional hospitals have ummmm mixed reputations.
Unfortunately this is very much the reality for lots of women in regional areas and it is very very unfair on them. But what you have described is basically how it stacks up.