Latissimus dorsi are your ‘lats’ muscles and this is a flat V shaped muscle connecting your arms and shoulders at the side to your vertebral column at the back and running down all the way to the hips where it shares attachments. It’s the largest muscle in your core and connects your upper and lower body providing protection to your spine and stabilizes it while enhancing body posture. It also strengthens and stabilizes your back, neck, shoulders and hips.
The lats are important in creating movement of the shoulder joint via extension, adduction and internal rotation. The lats also work together with other muscles in lateral flexion and extension of the lumbar spine (lower back).
With this all being said, the answer is a definite yes to if you should exercise them. Strong lats muscles will basically support you in most day-to-day chores or sports and protects you from injuries.