The problem is that everything changes everything. For a steel bearing, you have a specific steel grade, and a lube grade. You can fine tune that with each alloy, so you have a larger scale of standards. But that is also only a scale for bearings, nothing else. It is the end part.
Composites however, you have to take in to account the fiber, the areal weight, the weave, and sizing, the resin, the thickness, the loading, etc. Each singular component can be changed for each specific purpose. That is why most manufactures will give strength data for a uni-directional fabric, and they will then break down the numbers for the fiber, (or in case of pre-preg, fiber and resin), and then you have to recalculate for the specific fiber, AND part.
Also, for your original post, since a carbon tube can be built any number of ways, there is no spec for a tube. A PVC or HDPE tube uses one material, and that has a spec. Change the thickness or diameter, specs change, but in the end, material is the same. Composites is not meant for specific parts that can be mass produced. you have to know exactly what YOU want and what YOUR end product needs, and then you can spec out that tube for that part.
So for quality, there has to be testing done for consistency on the manufactures end of things. They have to spend the money to be able to produce a consistent part, and have it tested, and certified. Most companies will not do that unless the end user requires, and will pay for it. A plastic extruded PVC pipe will not change specs from one producer to another, using the same resin. But you can easily screw up composites.