Jesus, if you knew how many times my he's best friend's halfling fought from the back of my half orc NPC, well, I guess you'd not really be surprised, but maybe slightly amused?
I envision after being tired of "standing" the child will recline back with the chest strap, and jamming the metal bar directly on the vertibre with their full body weight.
Also note that a mounted character can travel at twice the top travel speed for an hour. It doesn't specify anything about what creature they're mounted on. And with the right feats they could be helpful. Imagine a tank with a Mounted Combatant feat riding the squishy wizard and absorbing all the attacks against them.