Random thoughts, but I can't be the only one, right? Behavior folks?
I know a lot of people like a horse with a lot of "try" or a lot of "heart" in him/her. IE, a horse that will keep working for you, even if things aren't exactly going according to plan or going perfectly and are difficult. Sometimes that difficulty is on the horse end, sometimes the rider end, and sometimes it's just a tough situation, like a stream with muddy banks, uncertain footing, and no good way to get around except by going through. Some of this could even fall under the category of bravery, I suppose.
I think that poor training stamps a lot of try and heart out of a lot of good horses. I see it in dogs too. Poor training can ruin an animal's willingness to work all too easily.
My horse was initially broke to ride by some random traditional horse-trainer in South TX. He was just another late-gelded untrained 4 year old that needed to be under saddle to be at all marketable. I don't think his training was overly harsh or in any way unusual or different from what many horses get. He got the basics. He was reprimanded when he did something wrong, and not reprimanded when he did the right thing. He's a little sensitive compared to some, but not as sensitive as others, so all in all, everything was fairly normal.
I got a horse that was terrified of doing the wrong thing though. Things he knew were right, he would do quickly and willingly, johhny-on-the-spot. Ask him something he didn't know the pat response to though (like to sidle up to a gate), and he'd get tense. He'd throw his head up in the air and either try to run off like a giraffe or try to pretend he couldn't 'hear' you at all and figuratively stuff his fingers in his ears. I think those are pretty familiar responses and things we see commonly in green horses or horses with less than perfect training.
He was so scared of the punishment for being 'wrong' that he refused to try. Flight, fight, or freeze kicked in. He didn't want to offer any behaviors or attempts to figure out what I wanted because he knew, from his previous training, that if they weren't the 'right' ones, he would be reprimanded. It's tough, and not entirely safe, to train a horse that is so scared of being wrong that his entire existence under saddle is in a state of anxiety. Fear is dangerous.
I spent the first year un-training that previous life experience. Teaching an animal that they will NOT be punished for trying to do what I want, even if their response is wrong to start with, is a slow process that can be very frustrating. The biggest hurdle is getting through to them that it is okay to try. Getting them to learn that trying, by its very self, will actually be rewarded rather than reprimanded, is the key. Baby steps. The tiniest baby steps ever. The least 'try' they will give you has to be rewarded to start. Once you have a horse willing to try to give you the right answer, it's too easy to simply guide them to the correct behavior and then only reward them for what it is you actually want.
My horse still gets anxious and worried when he doesn't know the right response or understand the question sometimes, but he lives to please, and I now have a horse that will try and try and try. He has a heart as big as TX and is utterly fearless about figuring out what crazy thing it is I want this time. Even when it goes against his natural instincts, he knows that so long as he keeps trying, he will be rewarded, and that there is no punishment for not getting it right on the first (or the fiftieth) try. Having a horse that trusts he will eventually figure out the right answer no matter how nutty the situation I've put him in seems (to him) is priceless. He knows I won't set him up to "lose", and if you can't lose, you can be a very, very brave pony indeed.
That is how my spooky green gelding became a horsie good citizen and will face all sorts of monsters (real and imaginary) and challenges just because he's asked to. Maybe it's sappy, but his "try" is my favorite thing about this horse, even though he didn't have any to begin with. Cookies if you stuck with it all.