OP's horse is nowhere near as bad as that REALLY poor one posted, BUT that's still not enough bone to support the horse's considerable muscle mass. Consider my horse - anglo arab, so bred from two "lighter" breeds, but he's 15.1 and I would BET his bone measures far more substantial than OP's horse. I've been told it's "adequate" for his height and weight - not "plenty", but "adequate".
Yes, IMO the grey appendix is also light on bone. I wouldn't say worse, because he's not as thick through the body OR as heavily muscled as the paint, but he is definitely light on bone.
IMO the appy is "adequate" rather than thick. I hate seeing chunky built horses with fine legs, it's not a conformation that lends itself to long-term soundness.
You want to see thick bone, look at the English (Gypsy, mostly, and some others) cobs. THEY are thick. More bone than strictly necessary for their weight. Why? Because they're expected to be the family horse, strong enough to carry grown men but small enough that children can saddle and mount.
Bear in mind a halter horse fitted for halter well enough to succeed at the upper levels won't be flexible in its muscles simply due to sheer muscle mass - so, you want him to do well at halter, AND performance, maybe performance halter would be a better path to go down.
For the record I'm not anti-halter at all, I just don't like what the AQHA (and to an extent, the equivalent in Australia) has done to the breed. We OWN a QH, he has significant soundness problems, and guess what? Tiny feet, less bone than my Anglo, and at least two inches taller - and significantly wider. We don't have the problem here to the same extent as can be found in the US but it IS still a problem.
And I think OP's horse is better than some Australian QH stallions, but that's still not enough bone.