My TB is your classic "mental" hot sensitive nervous wreck - on the ground, and ESPECIALLY with the wrong handler. She's come a long way but new is scary and scary is too much to bear. She's a rearer when she's pushed too far and certainly not an easy horse to handle. Too sensitive to hit, too over-the-top at times to ignore, and cold-backed to boot.
Under saddle, once she's warm and past the cold back, she's still a bit of a nervous spooky sensitive nut [I mean heck she's a red TB filly, what do you expect?], but she hasn't once offered to rear, and I have confronted her with some pretty scary situations. I haven't let anyone but me ride her yet because she's only had 10 or 11 rides [she's 2 1/2, I don't want to push her too far too young] and she's still so unsure of strangers that I'm not convinced she would allow someone else to get on her back.
Despite her sensitivity, nervousness and fizzyness, she is intended to be an event horse. Actually I find that the nervous sensitive ones, if they're brave as well [my girl is, with a confident rider], can make superb jumpers and eventers. It's one of the reasons TBs are so good for the sport - look at the Olympic eventers, the vast majority are Thoroughbreds with the odd TB/wb cross and occasional full warmblood. There are occasionally horses of other breeds that make it to the top as well but TBs and TB crosses are by far the vast majority.
And not one of them is an easy ride. They're all so sensitive, fed to overflowing with performance feed to give them the energy to compete at that level, and love their jobs SO much.
Working with your sensitive "crazy" TB will make you a far better rider, and depending on soundness and your horse's inherent ability, you're less likely to have to change horses when you get past about 3' [here, that's Prelim-ish].
My eventer is extremely lazy, and so quiet that he's actually part-leased by a beginner [mind, the beginner doesn't jump...], but point him at a large enough expanse of open space, or any kind of jump bigger than about 3', and he turns into a hot, forward, strong pain in the butt. I don't ride him XC in any less than a kimblewick and actually prefer to have him in a pelham. We SJ in a snaffle but he does bolt now and then on course! Even lazy horses can be hard to handle when jumping if they enjoy it enough to really excel.