To the original question: I started using my dominant (right) hand to cast, left hand to strip line and reel, when I first started casting single-handed. Like for most, that habit set in pretty hard. Casting double-handed, I could only strip line with my left hand.
Years later, at some point in my speycasting, I started to realize I could diagnose/debug various casting faults by comparing right vs. left side casts (I switch up hands, I do not do cack). By definition, one side is always better than the other at any given point in the cast. The more symmetrical the cast is -- ideally they'd be perfectly symmetrical, but they rarely are -- the easier this is to do. I noticed one thing creating asymmetry in the cast was the way I stripped line, as I always stripped with the left hand, and that meant a hand switch on one side, and the two sides were set up differently for the cast. So I forced myself to learn to strip on the other side, just to see if it made it easier to see what was going wrong earlier in the cast. Took about three weeks. In retrospect I don't think this really made much of a difference other than I like not bobbling the rod back and forth between hands.
All of which is a long-winded way of saying, in my experience, training the off-hand in these things is, in the long run, less effort and time than you'd think. Quite painful and requiring discipline in the short run so presumably discouraging for many.