How many folks out there, practice their katas "right and left"?
I picked up this practice 3 decades ago. For about 10 years I required my students to do kata "regular" and "mirror image." For one test you'd have to do Seichin "regular way" and Kanshu "mirror image." Next test you'd have to do Seisan "regular way" and Seichin "mirror image."
Recently I've changed the method to my madness. Along the lines of viewing Uechi kata as reference books and not story books... I now drill all the movements in the kata both ways. Before doing any kata I'll have two or three "sequences du jour" that I'll drill with the students. I'll tear the movements apart and practice the pieces, and then put them back together again in myriad ways. And as part of that drill process, I'll have students do those movements both "regular" and mirror image the way you would say do "hawk chases sparrow" in Seichin both ways. So yes... my students need to be able to do a Seisan jump from both sides. They need to be able to do a Uechi knee strike both ways. And yes... I train black belts to do the opening movement in Sanseiryu both ways - both simple and complex. Then I'll have them do the whole kata - just so they retain the material in "the reference book." On occasion I might make the students do the kata mirror image, but not so much any more. As long as they can do the sequences both ways, then the actual kata can stay as is and I don't have a problem with it.
My biggest issue is with the occasional dyslexic student. I had a female PhD polymer chemist from Dupont who was a student of mine for a few years - all the way to shodan. When I had her doing the kata both ways, she'd sometimes get lost in the middle of a form. When working with her I had to touch her left arm and say "left punch." That was just her brain wiring. It was amusing, as she was otherwise brilliant. (Some think Einstein was dyslexic.)
Mostly it's wise to do this to keep balance in the body. To do otherwise is to risk certain kinds of injuries or "back owies" that can come from repetitive uneven forces on the body. Good athletes learn to do techniques both ways. At age 40 I taught myself to be a switch hitter in the batting cage. It's fun... Keeps my body honest. And it also keeps the brain wired multiple ways to do the same thing, which can be very helpful for stroke recovery. Plus... you never know when you're going to face a southpaw. Having the reverse perspective can be handy.
I work very hard to train the body evenly in the weight room. Same principles apply.