Don't do them.
One of my students (and Judo Black belt) used to practice in a Dojo in a large Aikido organization. Someone observed that a large percentage of the older Sr. students were 'all busted up'. They concluded it must have been from the years of brakfalls. They no longer do them, and the latest explanation is that you can practice longer/harder without the breakfalls.
This is their conclusion, without much of a study it seems. That isn't to say that the statement isn't correct with the individuals mentioned. While I don't think it is necessary to train "high breakfalls" every class I think it is an important skill to keep up. I have been training Aikido for 19 years and while I don't take them all the time I do not suffer any ill effects from them. Why one gets 'all busted up' is more complicated than taking "high breakfalls." How they learned to do them to start with, whether or not they took the time to heal from any injury they may have sustained (whether from taking falls or from any other part of their life) as well as their mental well being and temperament when training. No, I don't believe that "high breakfalls" need to be or should be practiced every class but I also do not believe that we can say definitively that they will get you 'all busted up.'