Baucher?

What is the purpose of the Baucher? Bit, especially what is the purpose behind the extra ring that holds the cheekpieces? As far as I know, they are NOT leverage bits, though some people believe so.

I, personally am scared of single-jointed bits of any kind, or for that matter any bit that has a 'nutcracker' action- squeezing/pinching the mouth/bars, poking the roof of the mouth ect. Could this possibly be a safer option?

Just like snaffles, bauchers come in both single-jointed and double-jointed/lozenge mouthpieces (and heck, even waterfords, too!).

A baucher won't create poll pressure unless the ring attached to the mouthpiece is shaped such that the reins are prevented from sliding. With the configurations pictured in the OP, rein pressure would pull the bit straight in the direction of pressure, as the reins are not fixed at the bottom of the bit ring, meaning that no poll pressure would be applied.

I believe that they are intended to keep the bit steadier in the horse's mouth. And like any snaffle, you can get them in single jointed or double jointed mouth pieces.