I agree, running is much higher impact on your joints, much more likely to cause an injury. Shin splints is the most common injury among new runners. If you are jumping rope correctly, your feet are virtually never more than 2" off the ground... very little impact.Why would you get shin splints if you are on the balls of your feet. You are much more likely to get shin splints from running especially since a lot of people run landing on their heels. Of course you can get out of breath jumping rope. Ever heard of double unders? They'll get you out of breath and you can sprint whilst jumping rope. If you aren't getting out of breath then you aren't jumping rope fast enough.
jumproping only works for boxing and has no crossover benefits for MMA. Not only that, but its a gay activity for little girls and you aint no fairy, are you? Just Bleed and flip tires and swing sledgehammers.