I've trained all of my horses to do flying changes the same way and they never "cantered around crooked on the forehand." Maybe I just got lucky but the horses I trained did full changes and didn't change late over the pole. It was becasue they were balanced and ready for the change. Now, admittedly, my experience is more in hunters than dressage though I am breaking into that now. While my horses could do lead changes at any point in the course on command, the actual point of what I would call success was asking for the correct lead over the jump and getting it on the landing and being able to reblance before the corner. As I indicated, and I think you agree, albeit maybe using different terms, the horse has to be balanced and have impulsion, or if you prefer, has to be working from behind. If the horse doesn't have this, agreed, you aren't going to get any type of decent lead change, simple or otherwise. Some horses, not all, will anticipate a change if you do the exercise long enough which is what I meant on the shortened simple change. Agreed, there needs to be 4-5 steps or so and a rebalancing, if it is needed, but, if the horse is already balanced in the downward transition from canter to trot or canter to walk, you don't HAVE to put 4-5 trot/walk steps in between.
As for the pole, it gives the horse a momentary suspension. When I said shift weight, I am not talking about doing a two-point over the pole or overly shifting weight from side to side. It may be no more than simply adding a little more weight, by lengthening the leg, into the new inside iron or just a slight shift of the seat bone in the saddle as the opposite aid is applied.
My present horse (new by 3 weeks) is a proverbial balance nightmare right now but he is also very green. I won't and wouldn't even think of trying to do a simple change with him right now; he could do it but as you indicated, it wouldn't be pretty. He needs complete rebalancing after each transition, which he is getting better and better at, but we still have a ways to go before I attempt even a simple change.