Untrue. There are many, many, many compounds that do not involve carbon in any way, shape or form. You are correct in that organic compounds all have carbon in them, but that's only because organic compounds are defined partly by the presence of carbon.
The reason carbon is found in many places on our planet is simply that it is in the top 12 most abundant elements on the planet. It exists in every domain of life, but that doesn't mean it exists everywhere, and it doesn't mean it's the future of engineering. By your logic, oxygen and hydrogen would be the primary components of bicycles due to their prevalence in nature.
Indeed Carbon is the 4th most abundant element in the Universe. But Hydrogen is the most abundant.
No, my logic does not make any such claim of its wide use solely because it's abundant element. It's prevalence isn't only reason.
The element has an affinity in forming stable compounds with other structures. Because of this Carbon forms the largest majority of all compounds in the Universe. The structure of Carbon and compounds it can form makes it extremely useful in building "stuff" up. From simple organic compounds like Methane all the way up to Biology.
Because of this, Carbon can build up chains of itself, strong ones at that, into molecules of so called Polymers.
The Future of Engineering is only limited by human ingenuity. Natural Selection provides a convenient template for most common and workable denominator.
Re. 3D printing.
This is simply the automation of what can/is done by hand. The material is a prototype model. I don't expect such a model to be that useful or durable though. Just because it comes out of a machine doesn't make it better. Carbon frame production is already a form of rudimentary 3D printing, but done by hand.
It's just not very effective to build a frame this way.
Same argument applies to metal frame production. Instead of printing an entire frame using an alloy material, don't ask me how, the most plausible and closest explanation would be machining it instead. Again such a method proves very wasteful and expensive due to recycling involved. Assembling prefabricated tubes of Alloy or Carbon are simply most direct and cheap ways of building frames.