The term "shotgun trained" has come up a few times - I'm guessing that means they were trained in a hurry, just enough to call them "broke" and get them sold. That's a pretty close definition. You could add the thought about just getting them enough training to do one job (of course that might be more properly called "rifle training" ).
Apart from not standing for mounting up, what other issues tend to come up with these kinds of horses? Painting with too broad a brush is possible, here, but some other common issues are not teaching the basics of "being a horse" through thoughtful ground work. This would include difficulty in bringing in from a pasture; failure to tie quietly for grooming; failure to stand quietly for vet/farrier; poor leading manners; etc.
Then there are holes in fundamental work under saddle, such as not knowing the meaning of cues from the natural aids (hand, seat, and leg). Many are not allowed to canter, only gait (under the flawed assumption that work at the canter compromises gait quality).
As a group, it sounds like they're all fine trail horses, but maybe they have the same set of weaknesses. Horses from the same general, geopraphic area will often exhibit the same weaknesses. Culture counts. Horses bred and trained for the show ring often have some of the biggest issues. Close behind are the "backyard horses."
If that's the case, here's a few other things about mine that maybe you all have seen in your horses too:
In addition to not standing for tacking/mounting is also head-shy, and hard to catch. He doesn't know how to lunge outside a pen either. No surprises here, but this is a relatively easy one to fix.
On the plus side, he leads, loads, picks up his feet and stands for the farrier.
He'll stand tied, but not happily. He'll learn if you give him the chance. This means bring the horse up, tie him, and then go about your business for a few hours. In the beginning keep a weather eye on the horse for difficulties, but he'll quickly learn that this is normal.
What I've noticed as far as correcting the head-shyness and the catching is that setting aside the time (even hours) to work slowly has been much more effective than trying to force him to do something "cowboy style." The mantra if any good horseman is "I have time."
There have been times when I've had to spend 2+ hours walking him down, back and forth across the pasture, until he lets me catch him. You're playing his "game" when you do this. Pick a system of training and the make the horse play your "game."
As long as I catch him, even for a pat, every single day, he stays (relatively) easy to work with. Normal behavior for most horses.
If I give him a break, he gets more difficult again.