Flexibility and mobility work should support your strength work, not replace it. The terms flexibility and mobility are popular and rightfully so. You need to have requisite flexibility and movement quality to perform at your best. That being said, there's no substitute for responsible strength training when it comes to preparing the human body for durability.
Athletes who stray too far from regularly lifting heavy stuff the right way are setting themselves up for injury issues. Not only is mechanical loading (lifting, pulling, pushing, holding heavy stuff) key to muscle strength, growth and health, but it's key to the health and durability of the body's support structures. Your bones, tendons and ligaments respond to resistance training by becoming more durable as well. The two things that an athlete needs for success are sport skills and health. Make fundamental strength training exercises like squat, lunge, deadlift, pull-up, chin-up, push-up and rows your priority to train for athletic durability.