Meh, tomayto, tomahto. Sort of. I don’t, absolutely don’t, use a renewed aid each stride for lateral work at any level. I find it klunky, repetitive, nagging, irritating, and interruptive of flow of the movement and of the gait. You don’t even need to do it to teach it in hand. For example, to teach the ToF, you would position yourself appropriately and raise your whip, then tap to get the horse to respond. When there is a response of a single step, you would lower the whip and praise the horse. Repeat until the horse understands that ONE step away from the whip earns praise. The horse, all by itself, will notice the change in posture of the whip. From there it is dead simple to leave your whip raised for a successive step. Horses are a lot smarter than we give them credit for. We don’t need to spoon feed them anything every stride. Teaching it under saddle is the same. We don’t ask for a whole long side/open side of the circle/diagonal when we start teaching it, we ask for one step until the horse understands and then we ask for two by maintaining our seat, and then 3 and so on.
That said, I am a lazy rider and expect my horses to go by themselves. I want them wanting to move, not wanting to stop.
Oh hey, here’s another way to think about it. When we teach a horse to longe, do we nag it every stride by waving our whip around, or do we ask with the whip and then leave it be at the “go level” and allow the horse to move all by itself without a regular reminder every stride? For me, it’s the same answer whether asking the horse to go forwards, sideways, or backwards, no nagging allowed