I have three TWH's and still have an Arab who is the best horse for young children a person could ask for.
For those folks considering going gaited, whatever breed you choose:
PLEASE REMEMBER the same gait may not feel the same on different horses due to their skeletal structure.
The running walk on my tall lanky athletic built TWH feels very different than it does on my "Quarter Horse Stout" shorter coupled TWH.
My best ride for my back is the Fella in my avatar that does the dreaded stepping pace smoother than some TWH's can perform the running walk.
He's the guy I bought 19+ years ago and I sure am glad I was gait-stupid because he's been a horse that only comes around once in a lifetime. Even my trimmer says he'd be a wealthy man if he could find 100 horses like this one
Anyway, the same gait can feel different on each horse, so don't give up on a particular breed because the first few you try out don't feel comfortable to your specific issues