I'm excited to see your guy grow up! I've only heard a few things about GGs in the past. But I agree with the OP that ASB get sold short. Why do ASB get a bad rap? I have heard they do well as saddle horses (even dressage/jumping). But I have also heard they are known to have weak backs?
The American Saddlebred is probably currently best known for it's performance in Saddleseat, as such, it seems to have been forgotten by a lot of riders from other disciplines, in spite of once being a popular mount (according to some long time breed fans they faded when the European Warmbloods started to make their debut here in North America, not necessarily for lesser ability, but because they were no longer the "fad of the day"... I'm not sure that is entirely accurate, but that is what I have been told)
The "modern" Saddlebred has, in some cases been so overly bred with amount of "trot" being placed above conformation that the breed is now becoming known for serious conformation faults such as lordosis (sway back), crooked legs, long loins, long backs, light bone etc. by breeders who just don't "know better". These horses often end up more or less low level horses, even in Saddleseat... And so they are often what a base majority of sport riders see trying "new" things, and being, obviously unimpressed.
This type of breeding is not done by the breeders at the top of the discipline though, and so you can find well built individuals without too much trouble. The issue can be purchasing them before they have been trained to move incorrectly for sport - Saddleseat shows off the horse's scope, and athleticsm but not in the same way a Dressage horse or Jumper will. As a result once they are trained for Saddleseat they would need to undergo a lot of retraining to teach them how to move correctly for their new job. There are a few breeders who do not breed for the show ring, and a few SS breeders who will see a foal has less talent for the show ring and aim it for other disciplines... Many will still train it for Saddleseat because that's all they really know.
Less educated people will see the horse moving "upsidedown" and with short high strides and think the horse is ill suited for anything else.
In reality, many Saddlebreds are quite capable of excelling in many different disciplines (the same conformation which allows them to move snappy and high also gives them scope for fences, and most are also able to lengthen their stride as well), and do so when they have been properly conditioned for their job, the thing is, less than 3000 Saddlebreds are registered every year in the US (compared to 300,000 or so Quarter Horses , 100,000 or so Paints, 100,000 or so TBs - I used to have the exact stats, but they aren't handy) and most of those are being used for Saddleseat or other ASHA breed showing, as until recently ASHA (American Saddlebred Horse Association) did not actively promote the breed for open divisions or reward members for showing in open divisions. (In the last few years they have begun an open division reward program to promote what is otherwise a quickly disappearing breed to riders outside the breed)
There are some breed fans who are actively trying to get ASB horses back into the open divisions with success, and hopefully this will help win back some popularity for what is really a lovely breed option!
Sorry for the novel... Quite obviously I really like Saddlebreds