Sorry, but you’ve defined nonobjective art. Art without a subject, or more precisely, art that does not depict an object is "nonobjective" (no object).

Abstract art is any art that does not attempt to be realistic in the sense of holding a mirror up to the world and copying the physical forms accurately. Abstract art strips forms down to the essentials in an attempt to capture the essence of things or provide a new perspective on them. Nonobjective art is by definition abstract (a "realistic" depiction of nothing?), but then so is plenty of objective art. A Pablo Picasso painting of a woman or a Piet Mondrian painting of a tree are quite abstract while still having a definite subject matter.
Eponymous –Of course Picasso was representing things in his paintings and of course he was looking at real objects in a new way – these things are not in dispute. What is are what terms we use to define what Picasso was doing. It’s not the analysis, but the fact that we are defining the terms differently. Abstract is in some quarters used as a synonym for nonobjective, true, but in others abstract is a broader term encompassing both representational and nonrepresentational art. I prefer the latter definition because it does not make much sense to me to define abstract in such a narrow sense, because how could you not think "abstract" when you see the work of Picasso or Mondrian (his earlier, representational work)? Picasso and Mondrian and Reinhart and Motherwell all come from the same general tradition, the twentieth century exploration of means of representation other than realism and copying the physical world – abstraction.
Of course the term "20th century transportation" is inadequate and overly broad – but it is accurate. If I could change the analogy a bit to remove the bicycle, all the things you cited are alike in important ways: motorized wheeled vehicles, gasoline powered, metal, mass produced. They are all different and each deserves to be considered on their own merits, but they are all similar in essential ways. The same with the cubists, futurists, et al. They all are different in many ways, and opposed to each other in some ways, but we can look at them all and note their similarities, especially when compared to the art of other centuries. And one of the key differences that sets 20th century visual art apart, and makes it one of the most exciting and vital IMO artistic periods, is abstraction.

I see what you are saying, and I agree, that there is a need for a specific term to describe non-representational art, but that term already exists: non-objective. I think that term is more useful and precise for many reasons. I find it helps my students (who are largely ignorant of visual art, especially paintings that don’t "look like stuff") understand that there are some paintings that represent objects and others that do not, and all paintings that look funny are not alike. And without the term abstract as that catch-all, what else is there to describe the 20th century trend away from copying forms as they appear to the eye? What words do we use to describe the links between disparate 20th century art movements and the differences between those and the ones of previous centuries? Picasso, as you said, is most definitely representational, but it seems quite inadequate and silly to use representational as a catch-all to label everything from cubism to photorealism. What makes Picasso or any number of 20th century masters from the Renaissance or Baroque masters? Abstraction. There are some paintings by, for example, Kandinsky which are representational, others which are not, yet both types of paintings are quite similar in style. What word do you use to note those similarities of style? Abstraction.

And don’t worry, nothing you’ve said could be remotely considered an attack. This is fun. :)