I am watching this thread to learn also. Does it make any difference that there is no front coulter? (No defined left wall ?). The rear coulter also appears to be quite a bit to the left of the shin. FWJ I have learned is a big proponent of having coulters.
Some people choose to plow without coulters. I prefer them, ESPECIALLY so in sod or where crop residue is present. I've never encountered any negative problems from using coulters and have enjoyed many beneficial advantages, so yes, I definately advocate having them.
Old school thought was the coulter should cut deep enough to form the furrow wall. If a plow has good shins, that isn't so much a factor. They're MOSTLY for cutting surface trash so the plow doesn't "plug". Also, cutting trash help the plow to cover crop residue, leaving a cleaner plowed surface.
The coulter should be SLIGHTLY to the left of the shin, maybe 3/8" to 1/2". With coverboards (this plow DOES NOT have) the coulter would be set even further left. (5/8" to 1", depending on results)
In HARD dry ground, coulters need to run shallow. Too deep and they tend to serve as sort of an improptu "gauge wheel", holding the plow up, preventing it from easily reaching desired depth. A single coulter on the rear COULD cause the problems described in this thread, especially so if the ground is hard. In "normal" conditions (whatever "normal" is....) and with a decent amount of soil moisture (to "soften" the ground) a single coulter shouldn't make significant difference.
But....it would take all of a couple minutes to drop that coulter off the plow and give it a whirl. That MIGHT be a worthwhile experement.