Isn't a visit to a (good) physio worth the cost if theres even a chance that they can address the underlying cause of your pain and give you the tools to work on to reduce/remove the cause of your pain?
This potentially could happen even before your mri appointment comes around and certainly LONG before you get to see a ortho knee specialist
Your non knee specialist GP will likely reach for the cortisone needle.
An orthopedic surgeon.. being a surgeon will most likely reach for the knife.
A (good) physio will help you understand your treatment options, be able to diagnose the injury/cause of pain and if surgery is something you still want/need to explore then they will be able to give you pre-op help that will speed your recovery and likely reduce your post-op visit requirement/costs anyway.
Ultimately you're going to have to see a physio at some point, may as well see a (good) physio now