Biology is way ahead of us in producing stuff with useful properties. Nanotubes are nothing new, some structures in your body are made out of nanotubes, take e.g. your tooth enamel. The nanotubes there can become depleted of minerals after eating foods containing acids, but they'll refill in about an hour's time. This is why your dentist will tell you to not brush your teeth immediately after eating a meal. Empty nanotubes are easily damaged, they won't be replaced so you'll have permanent mineral loss.
Diamonds crystals have no known use for ling organisms and they are also hard to grow in a biological setting. You have to keep in mind here that humans are used to build structures on a macroscopic scale. Machines that we build will have smallest functional parts that are still enormously large when viewed at the atomic scale. This then means that our machines are prone to degradation due the system accumulating damage at scales that are smaller than the smallest accessible scale.
Biological systems don't have this problem because the relevant machine parts here are at the molecular scale. Damage at smaller scales requires bonds between atoms to be broken which requires very high energies. Also the systems themselves are small enough to intervene at that scale. So, the reason why we want to use diamond (a strong material that doesn't degrade) is not relevant for biological systems.
Here we also need to keep in mind that biological systems are constantly at work to maintain themselves. So, it's not like any machine that we build that only very occasionally will need downtime for maintenance and still we'll take it for granted that it will degrade over time. A biological system will almost immediately fall apart if the internal self maintenance processes were to stop. It's the equilibrium between breakdown and rebuilding that keeps your body in shape. Increasing the demand for rebuilding by exercising will shift the balance such that your body becomes stronger.