Why do optometrists do things an ophthalmologist should do, and vice versa?

Any thoughts on optometrists treating non-refractive eye problems?

Could any one compare the refraction abilities of an ophthalmologist
vs. those of an optometrist, or are they both equal? And why do they
let optometrists --in the US-- treat things like glaucoma, cataracts,
convergence disorders, accomadation pathologies, conjunctivitides,
etc.? Optometrists should refer their patients to
one who is more qualified to treat them, ie an ophthalmologist. And
why do ophthalmologists refract patients for lenses, or treat low
vision? They too should refer their patients to one who is more
qualified to treat them, ie an optometrist. Both types of eye doctors
have their place in the healthcare system...but they shouldn't do each
other's jobs, it's less productive and could lead to misadventures.

Good questions, interesting topic.
I think that ophthalmologists can do all the things an optometrist can
do, i.e. refract patients, because theoretically they have more
training than an optometrist plus the additional training needed for
ophthalmology, therefore they are 'qualified' for anything an
optometrist is. In real terms, though, I think you are right about
optometrists being more experienced with refraction and thereby better
specialized and accomplished refractionists. So if you were to compare
the overall refractive ability of an ophthalmologist versus an
optometrist the latter would be higher. Also, I heard that
optometrists can take additional training mid-way through their career
to give them some of the qualifications of an ophthalmologist, so they
have the legal ability to prescribe and medicate patients with
medicine or eye drops and stuff like that for people with eye
pathologies like glaucoma and cataracts.
You may be right about non-specialized people doing the job that in an
ideal world a specialized person should do, but in the profession I
think there is often a lack of 'ideal', for example all the
ophthalmologists might be too busy dealing with other cases so they
have to let the next best qualified person, i.e. an optometrist, do
the job they would have otherwise done.

I meant 'because theoretically they have exactly the same training as
an optometrist'