The point of mobility work is just to keep your structural balance in check and ensure all the muscles are healthy and strong. Mobile muscle merely means that the muscle is strong, healthy and works like it's supposed to work.
When all the muscles in the body are mobile, compound exercises like the pull ups and bench press will strengthen all the activated muscles to their full potential.
When the body is out of balance, the form is never what it is supposed to be which leads to even more imbalances in the body. This eventually leads to injuries.
Good structural balance and healthy levels of mobility will maximize the long term success since your body will get stronger as a whole and there will be no weak links to slow you down.