I seems like you answered your own question.

In the USA, states regulate driving requirements and some would indeed
restrict driving for similarly visually impaired persons.  (The
following is based on USA "right side road" driving) From a practical
viewpoint, if it is your left eye that is non-seeing, you would not be
able to see objects in your left side-view mirror. You could, of course,
turn your whole head and use the right eye, or turn the other way and
look out the back. Either way, there is indeed a safety issue as:

1. you lack stereoscopic depth perception
2. your reaction time is decreased by the time it takes you to turn, see
and react, during which time you are not seeing straight ahead.

Then, of course, there is the issue of "legal limitation" enforced by
the state and "moral and ethical" limitation based on your personal
experience and concerns.

How about fixing the diplopia?

Meanwhile, if you're a really good attentive driver, you are probable
less of a risk than the moron who nearly hit me this morning on my way
to work on my bicycle. She was quite busy talking on her cell phone and
not paying attention to the stop sign or crosswalk or ME, wearing a
bright red helmet and yellow safety vest.

--LB, OD

Peter -- Where I live, the rule is that you shouldn't drive for three months
following a switch from binocular to monocular vision. This is to allow time
to adapt to judging depth and distances, and to get used to turning your
head to see all around you. Once you are used to compensating for it,
driving with monocular vision should not be a problem - plenty of people do
it all the time. In my opinion the depth judgement is not the hardest part
of it, but learning to look around (turn your head etc) to eliminate "blind
spots".

Of course if you don't feel comfortable, don't drive!

Dom