I think that's a great idea! What I also would like to look into is something like a cowboy challenge of sorts. I think that is a great basis for pretty much everything and a horse can never be bomb proof enough (to put this into perspective, my boy is rather spooky at the moment).
I've read in other threads that horses can be too tall for certain disciplines and am kinda pondering on that. I mean, obviously, there is advantages and disadvantages, but i think every horse can be a good barrel racer, Western pleasure mount etc. Or not?
The training for trail or cowboy challenges would require him to learn to accept a lot of new things, could be really great for him desensitization wise.
There is merit to the too tall or short part. You don't want a 16.3 cutting horse for example (there are exceptions though in every sport) nor will you often see a 14 hander showing WP. It's not that they can't do it, just that they aren't ideal and at the higher levels if they aren't the ideal you won't get looked at most likely. For me that never stopped me from trying to do everything with mine. My old lady Jana is a great example, she's just at 15hh, formally a reiner but I did it all with her, WP, HUS, Jumping, Barrels/Poles/Flags, Show trail, western riding, showmanship with her was really fun - I loved when we got a pattern with more than a 360 pivot, the ol' reining horse can spin herself silly, I could run and turn with her.
Same thing with my old man Hondo - sadly the all-arounder is not as common these days but we did it all with him too, he has AQHA points (and other titles) in 8 different events.
Depending on what level you are wanting to compete at, why not try a bit of everything and see what fits? Perhaps find a local play day show and just try it all for fun. One of our local 4-H clubs has a few 'practice' shows each year as a club fundraiser, no payback just ribbons, everyone wears jeans & t-shirts and uses their training saddles, ride all day for $20 - so everyone close, kid, amateur or pro alike all go to school. It's nice to just spend a little money and have some fun, chance to see how youngsters handle the show pressures on a less stressful level and a good opportunity to find where strengths & weaknesses lie.