Single joint snaffles have an undeserved bad reputation.
First, many people think they fold and then will poke the roof of the mouth. That isn't how it works.
"When tension was applied to the reins, the mouthpiece pressed more deeply into the tongue, thereby causing the joint to move away from the palate. Single-jointed bits are usually described as having a nutcracker-like action, the implication being that when tension is applied to the reins, the angle between the arms of the mouthpiece closes and the joint is pushed toward the palate. In our study, any nutcracker effect that tended to push the joint toward the palate was more than offset by indentation of the tongue."
- Bitting: The Inside Story by Hilary M. Clayton, BVMS, PHD, MRCVS http://horseproblems.com.au/Bits/USDF_Dec05.pdf
However, Clayton is wrong about what the nutcracker effect means. Nutcrackers are not used to poke nuts. They are levers used to crush nuts. If you pull back hard on both reins with a snaffle when the horse's head is stretched out, you CAN catch the cheek between the metal and the molars, crushing the cheek and bruising or cutting the inside of the cheek high up in the mouth.
From Tom Robert's book "Horse Control - the Bit".
The solution is not to pull back hard when the horse has its head stretched out.
French links are not much better, because they punish the tongue:
With a snaffle, you can pull back with both reins, but need to do so gently - and that is true with single or double joint snaffles.
If you want to use both reins when your horse's head is extended, then a good curb bit is gentler on the mouth. The design of a curb bit means it rotates. It does not go straight back in the horse's mouth. Since it is rotating, it always applies pressure against the tongue and molars. That is the gentlest place to apply pressure, and also the most effective. Curb bits get a bad rap from people who think they work via leverage. They do not. They work by rotating in the mouth and thus applying pressure where it ought to be.