Well of course you can benefit from dexterity! Proprioception, or the sense of the body in motion, is a fundamental sense needed to ensure maximal performance and intuitive reflex response. Like a cat falling from a building, the benefits of having a strong personal awareness are vast.
Improving your balance will, for example, reduce your risk of injury during physical activities such as soccer or running. In fact, as you age, this balance will also help to reduce your risk of injury even in daily life. It's never too late to train your natural perception, and you won't regret it.
Your sense of balance improves general athletic performance, your ability to use the muscle you already have to its highest potential, to make the most efficient motions. The automatic use of your stabilizing muscles will become natural after a little training, and in this case a little goes a long way.
Balance in humans is controlled by three primary systems, the vestibular system, the somatosensory system, and the visual system. The vestibular system is your natural perception of equilibrium, based on the fluid in your ears, your ears send signals to your brain indicating acceleration and alignment. In the somatosensory system (primarily your spine), you're informed of the relative location and kinetic energy in your joints and skin relative to other parts. Finally, the brain automatically checks balance visually, try some balance activity with your eyes closed to find out just how significant this part really is.
There are many fun balance tools, such as balance boards, slacklines, and medicine balls. You can use these to gain dramatic increases in balance in a relatively short span of time. I found the balance board to be the most amusing to me personally. If it gets too easy, you can combine the tools into unique exercises together, such as abandoning the roller of the balance board and using a medicine ball instead (warning: dangerous!), balancing with only one foot on the ball, or moving the ball around your center of gravity during a different exercise.