Some horses respond well to poll pressure. Snaffles are not the end-all of bits.
I've used the gag bit,
and rode tonight in one similar to the second. My mare has always preferred one-link snaffles to 2-link snaffles, and she did OK in the gag bit. She did better in it than in a snaffle because her trick of getting the bit in her teeth didn't work - there was no escaping the pressure on the poll.
I then moved her to a bit like this:
It took a little ground work and a few rides to get her used to the curb strap, but she has done well in this bit. About my only complaint is that during a trail ride, she'll sometimes decide to chomp on the bit. Doesn't seem to harm her or the bit, but it annoys me.
My last two rides on her, I've tried this bit:
She neck reins better in the previous bit, but she likes playing with the copper rollers on this one - and that is NOT as annoying as when she plays with the whole darn bit.
I don't consider any of them to be harsh bits. Some horses like one bit better than the other. I like going outside the mouth to add pressure on the poll instead of going harsher in the mouth with a more severe snaffle. I also don't think a snaffle the horse is willing to fight is as gentle, long term, as a curb bit the horse responds to right away.
If I could only own one of the three bits, I'd go with the middle one -even if it annoys me when Mia plays chomp the bit with it. She is responsive in it, neck reins best in it, and it seems the most comfortable to her. But I do like the little copper rollers on the third bit...