It wasn't important at all to me. I went public and got a private room. The option was there for DH to stay, but we decided for him to leave. DD was born 5:20 pm. I was admitted to the ward about 8:30. Mum left then, and DH left about an hour later. Baby and I slept all night and he was back at about 6:30am. I was offered 10am discharge and if I knew then what I know now, I'd have taken it. Home is so much more restful than hospital.
That doesn't seem so bad.

Do you have to use PHI for a private room or so they just allocate according to what's available?

I'm wondering if I'm also being seduced by the idea of being transferred to a lovely hotel.... but I'm still not sure it's worth the 000s for that. I'd still just rather go home. We have the comfiest mattress in the world

Thanks for everyone's input. It's an interesting dilemma for a woman who'd rather just birth at home.