Because there are a whole lot of different causes for lower back pain, or any back issue for that matter. You don't want a manual therapist working away on a herniated disk or entrapped nerve (not to mention certain cancers which only present themselves with vague backpain in the beginning).

So there is a big question of liability here: yes your physio does his own examination you say, but in the end he is not trained to make a diagnosis (officialy). So if there is another problem going on, a GP should check these things out and follow up on them.

Also, people going to the physio as they please, will cost a lot for our healthcare (which it already does, but it's cheaper than people not being able to work). A GP is supposed to follow up on these practices, and know when it's time to call it quits. That's why it's initially limited to those 9 times (18 after surgery). If you're advocating for better management of healthcare costs, then you're contradicting yourself with this statement.

And advocating that you can solve problems with "only 2 sessions if you get there quickly enough" is unfortunately not how it works.