As a human, you are able to learn the general concept of leg and understand it, even if it is in a context you have never seen before and an object you've never seen or never seen used in that way before. Everything you learn, is also as part of a set of relations. Each of individual concept modified in a precise manner as you learn something new about any of them. A big part of human intelligence, from the simple naming of things, to the highest levels of science is taking parts of things you know and putting them together in novel ways.
In Neural nets this: https://arxiv.org/abs/1511.02799 is in line of what I mean.
I'd argue they are implicitly doing this.
> You can't run the classifier and find tires, then wheels, and then a car;
Why can't you run a classifier for tires, one for wheels, one for cars, then combine their outputs for a final classifier maybe based on a decision tree? You can train all the networks at the same time and it will give you a probability distributions for all 4 outputs (tires, wheels, cars, blended). What am I missing?
You're going to need large amounts of fine-grained labeled data for each category. You've also just manually determined some sort of (brittle) object ontology. What if there are only 3 tires? What if there are four tires on the road but no car? All sorts of edge cases, and all you've done is train a classifier for cars, not actually solved driving in any meaningful way.
Actually, that's pretty much what deep learning is doing. For instance: https://papers.nips.cc/paper/5027-zero-shot-learning-through...
That paper was from a few years ago, I think the state of the art is better now, but it's trying to do exactly what you're talking about. More broadly, what you're talking about falls under the umbrella of transfer learning (that is, a model's ability to learn helpful information about task Y by training on related task X, preferably by learning and sharing useful features.)