ABSOLUTELY--with one caveat: they must FIT well.
Now, while I don't believe that you have to use them for every workout, when you are working hard, at speed, or on the trail...YES.
Also, I don't really feel that they provide much, if any, tendon and suspensory support--if I can deform the boot with my hands, it will not be able to 'prevent' overextension of the leg. Just, no.
However, any horse, some more than others, can interfere and hit themselves, or whack into something, or get injured by the cart in an accident, or whatever.
One of the biggest reasons I try to use boots in speed workouts is from a very vivid accident that a Western rider had with her horse. She was prepping for barrel runs, no boots, and her horse overreached and severed his superficial and part of his deep digital flexor tendons. The horse was in a lot of pain, and was put down almost immediately, as she did not have the several thousand to rehab him. I don't remember if he had shoes on the hinds or not...but regardless, something that would have either not happened or would have been much less severe had he had boots or wraps on. The hoof would not have sliced right through the leg quite as easily.
Now, of course, minis are less likely to have such issues, but I don't need any sort of possibility of such a thing happening to my high level competition horse.
Finally, I use glue on shoes with one of my horses, and she sometimes interferes when on marathon, whipping through the obstacles. I know this because when I hoof blacked her and then ran a marathon, she came back with black marks on the inside of her fetlocks. That is unnecessary trauma that can be prevented by using boots.
If I can prevent any kind of injury to my horses while they are trying their hearts out for me, I will.
Here is a picture of Fascination wearing her sport boots...I don't quite remember which brand they are...but they fit ok. I had to cut them down, and then they slip, which is frustrating. But they don't rub her, so that is something. This was practicing for a combined driving event the week after.