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The key advantage of deep learning is its reliance on global optimization -- it learns a hierarchy of features jointly, which solves the fundamental problem of information loss. That's also one of its main weaknesses: it makes DL extremely inefficient due a lack of modularity.
To make backprop more efficient, you would need to make it modular and hierarchical, but you would need to that without compromising the very thing that has made it so successful. Not an easy challenge.
But many models do exploit modularity, where they train components separately, and then composing without propagating gradients everywhere. E.g. the deepmind RL agent in the grid cells paper
Or anything using word embeddings, or any embeddings.
I would argue that modularizing this would impose human perceived structure to the problem, thereby introducing the very bias it has successfully avoided so far.
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