I think there are still areas of vision that has to be researched, but there are also areas of research that has already been done that will be applied by the doctors as it becomes practical/possible.

I mean a lot of that stuff about the polaroids, red/green glasses, etc., is already known, but most optometrists wouldn't go into it either because you don't need it done on a routine eye exam, or because they don't know how to do it. Especially with the time=$ pace, a lot of stuff gets left out, that could be done.
Sure nutrition factors into your vision. Deficiencies, for example of vitamin A or b12, will definitely mess with your eyes. There are environment effects, like the prolonged near work we do in our society that probably affects development of the eye and its function. How eyes respond to certain things also vary from person to person.
There are weird problems out there with eyes... vision is a very complicated thing. I agree that binocular vision can be trained, and that can improve your perception for things like sports. There are exercises that can be done for the eyes to improve binocularity, like the "pencil push-up"... you see this one kicking around in some books of magic solutions, mixed in with crap like the Bates method, or that you should look at the sun, because light is good for your eyes (actually UV light exposure is associated with cataracts, and you can also severely damage your sight by staring at the sun too long, for example with eclipse viewing).
The accomodative system is also complicated, and it can also be trained with exercises. And accomodation is fundamentally linked with the binocular vision system...

In my opinion, astigmatism being caused by muscle imbalances is nonsense. I mean, eye anatomy has been studied for hundreds of years, and surgery is done on the extraocular muscles regularly. The muscles are attached to the sclera, and this is a quite rigid layer. It's erroneous to jump from the fact that astigmatism is caused by "mishaping" of the cornea, to assuming that it would also be caused by mishaping of the sclera.
You can quanitatively assess the shape of the cornea very accurately with a corneal topographer. By the way, astigmatism can also be caused by tilting of the lens inside your eye. As I was saying before, this Bates method concept has been adapted to ortho-K, where you wear a contact lens on your eye overnight and then your astigmatism is gone in the morning. But it's temporary. Or you can get laser surgery done to get rid of it. But your eyes can change with time, and the healing process is not 100% predictable. The Bates method just flattens your cornea temporarly.
Muscle exercises won't get rid of astigmatism. Tilting the head can be a behavioural thing in kids. Sometimes it is an adaptation to muscle imbalances, but this is to allow the eyes to align and move properly. For example (simplified), if you have a muscle problem with won't let you look right, you may adapt by turning your head to the right, so your muscles won't have to.
If the assumption that tilting your head helped you see better, then you should have noticed your vision getting worse when you straightened it out. I doubt you did. The only reason you'd have worse vision in this case would be if you had a muscle problem that didn't allow your eyes to work together with your head in a straight position (e.g. double vision, eye strain).

Yea, I agree that business and politics do influence what's taught in schools, but so does research. While research won't always give us perfect answers, I think over time knowledge develops and gets improved with experience. There are some things that aren't known yet, or perhaps that never will. There are also some things that are known, but that aren't in use or accepted by the mainstream.
But there is also some stuff that's just plain unsubstantiated garbage, that's passed off as "non-traditional knowledge". For example, old wives tales. Some of them may be true. Some may contain some truth. Some may be just plain wrong.
Yes, the source is a good way to judge the veracity of knowledge. But there are no infallible sources. And just because the source may be a good authority on one matter doesn't mean he is on others.