I seem to have very loose muscles and joints. Do I even need to bother with stretching before exercise?

Flexibility does seem important to the prevention of injury. Too much or too little flexibility may be a risk factor.

Scientists report warm-ups are more important than stretching to prevent sports injuries.Warm-up exercises, such as jogging, cycling, or imitating the motion of your sport, improves blood flow to muscles and speeds nerve impulses. It also delivers oxygen and
energy to muscles and removes waste products.

Warm-ups tell the body to get ready for exercise. The metabolism of muscles goes up, which makes the muscle fibers move against one another more smoothly. The result is increased joint range of motion. This is what we call flexibility.

You may not need more muscle or joint motion, but giving the muscles energy needed to contract and move smoothly will prepare you for activity. There may be an added benefit of injury prevention.