Your Physics is Wrong
Yes, the static friction between the wheel of the "cart" part of the ride vehicle and the ground is integral, but you don't understand that the large "spring" isn't there to center the cart at the end of the ride, but to dampen the oscillations of the cart in motion (yeah, we're talking about deceleration and whip-lash issues). It doesn't matter as far as loading when it comes to the final position of the cart, unless your talking from aesthetics pov. From an engineering standpoint having something for the cart to catch on wouldn't work due to the forces involved. To catch a car midway you'd have to stop the cart with a pretty sudden deceleration.
You're Not a Doctor, but perhaps play one on television.
A lot of injuries seen in ER are benign appearing, as the patient looks fine, only to worsen. Heck, we see tons of auto accidents in my ER and without a doubt the pain is worse on the second day, why we give them NSAIDs and counseling upon discharge if everything checks out and sadly we see the "lucid interval" folks who die of an undiagnosed brain bleed hours later because they thought everything was fine and showed up too late for neurosurg to operate. Looks are deceiving, that why proper evaluation is important, as well as preventive care. For OP, his condition could worsen many hours after the initial injury, I've seen soldiers during wartime continue to fight with injuries that would hobble a civilian. Is going to DLR war? Certainly, you got your catecholamines going and you got goals, like riding everything in the park, similar physiologically.
The mechanism of injury (bonus talking physics and medicine!) is different between a 3" horse bite and an impact injury from a metal cart that perhaps weight about 400 lbs, close to one quarter of a ton. That leg slowed a big heavy object, might be consider a crush injury by some, and though it looks "not that bad" on the surface, probably was enough force to have caused a lower leg fracture in an elderly person with osteoporosis as skin was broken by a blunt object.