Eschewing the strengthening of the brain during exercise might seem important, but any exercise of the body will include exercising the mind in some way. Those who believe a heavy workout shuts off their thinking processes have fooled themselves because it takes a great deal of mind control to continue exercising after the body has claimed it has had enough. Those who continue to work out should be able to recognize that their mind is overriding the natural control of their body to keep going, and it is only the strength of their mind that allows the process to continue.
People in professions that require regular workouts for strength training know this fact, but many outside those professions have yet to discover it. They might fail at first when attempting to push their muscles further, and they will have to build up their mind to do as much exercising as they need to reach their goal. Some will discover the strength of their mind on their own, but others will only find it with professional assistance.