Correctly and incorrectly mounting a bicycle
I do not buy the stressing argument, any sprint out of the saddle will stress many parts of your bike much more.
I would only be concerned with your stability during that mount and the risk of a fall in harder terrain when running. And the issue of possible slip of an unclipped left foot from a clipless pedal that may not support an unclipped foot enough - that depends on the type of your shoes and pedals.
The cyclocross mount that is most often taught is similar, but from the ground straight on the saddle. Only then you clip both of your feet. But if you dismounted with the usual technique to the left before, your cranks will be in the same position as you have them so if it is easier for you, I would continue using the cowboy mount.