Yeah, I really like that his head isn't being yanked up, that bugs me to death. No, the head bob isn't "necessary" but is a general breed characteristic and if your horse can do it, you're at least starting in the right area.
Hurley's right...the saddle's maybe looking a little wide. I say that because my old saddle looked just like that on Annie (my TWH) when I first got her. The saddle "came with" her, but it was way too wide. Kind of made her gait a little choppy. I noticed kind of a big difference when I got a saddle with a more narrow tree.