>The so called NPUs. Which are simplified GPUs optimized only for inference (forward passes). Such an algorithm would enable them to learn using only forward passes, hence without requiring backpropagation.

More importantly, you could build even simpler chips that physically implement a neural network out of analog circuits instead of emulating one with digital math.

This would use orders of magnitude less power, and also let you fit a larger network on the same amount of die space.