It is not the exercise itself that is bad, is either doing it too soon or too much.
High Impact Aerobics is still popular(I use to teach it, now I just do it), and yes there are chances for strains and sprains, if one warms up right, and prepares properly you can jump around for a long while.
I can only guess, like most other karate dojos, were the starjumps done right off the bat? If so, that is the problem. You should not just start using a muscle like that with out slowly warming it up first. Next, doing a hundred of them in a row is also wrong. Doing a hundred of any jumping exercise is just wrong.
This exercise I think is good for karate, if done with in reasong. It warms up the outer and inner leg muscles, the shoulders, and warms up the body. Just do it in reason, and warm up the muscle first. (ie lift your heels off the floor for 10 reps, then do some joint rotations, then do another set, then warm up some other joints, and then do another set, after that, you are more prepared, but each individual student should realize their limits and be careful and not over do it. The slightest pain felt, means that exercise is over for the day.
Take it from me, I have pulled both calf muscles badly from being stupid. If I had of followed my above advice my calfs might have been beter off.