Specific to your point, my local state run/funded hospital does offer several rooms with birthing pools and midwife lead births, they weren't pushy in any direction regarding birthing options and were generally positive on the experience, certainly didn't discourage the option.

Granted this is in a hospital, doctors are on hand if required and the option is removed if the pregnancy is higher risk, but a no-Doctor/kiddie-pool birth in and of itself isn't super remarkable.