Language confuses me a little. Is a leverae bit a shank bit with no curb/chin chain or strap?
Any bit that has a mechanical advantage is called a curb bit. The reins in all curbs are attached below the mouthpiece giving it a mechanical leverage advantage.
Any bit that has the reins coming out the mouthpiece, absolutely no mechanical advantage is called a snaffle.
I do not beleive that the bit makes a horse hard mouthed or soft but rather the way the rider handles the horse determines if the horse will be soft mouthed or not.
I absolutely hate the rubber mouthed bit, the plastic as well.
I use to start all horses in a side pull, a simple leather across the nose, but had a bad accident with a horse and since then I only use a snaffle BUT with a running martingale at first. Again I had a accident with the snaffle so I ran a curb for a little while until I had control of the horse then dropped back to the snaffle.
Again a hard or soft mouthed horse is the result of a riders hands and not the bit.
Alot of the very mild bits actually make for a hard mouthed horse because the horse doesn't respect them and you end up holding the reins to hard.
I don't beleive in contact all the time but rather the reins are for backup after the other aids fail. Ride with your legs, your butt and use the weight of the reins to signal the horse and only use an actually pull when all else fails