Bill Tindall, E.Tn.
The coped miter is advocated as a better solution for it will cover any opening of the joint over time. I suspect this observation comes from examining antiques where the miter on a door bead has opened over centuries.
There are factors that make the potential deficiency of the simple miter, as you are doing, unlikely to occur. Your frame members are not very wide, the lumber is KD and this piece will live a sheltered life in a modest range of humidity changes. Our kitchen cabinet doors are mitered this way and the have not perceptibly opened after many years.
I believe many problems observed in antiques resulted from building with wood that was not as stable as what we have available today. I'll wager in a pinch furniture was built from wood not sufficiently dry. At best the wood was air dried and it is a fact that for some years this wood responds to humidity changes more than KD wood. Finally, it was not uncommon for furniture to go out of style, do service in the barn or chicken house and return to the home when fashion changed again. (This humidity experience could be stressful.) Out cherry dining table was rescued from service as a work bench.