> It distracts from what is actually helping which is using different functions with nicer behaving gradients, e.g., the Huber loss instead of quadratic.

Fully agree. It's not the "fault" of Backprop. It does what you tell it to do, find the direction in which your loss is reduced the most. If the first layers get no signal because the gradient vanishes, then the reason is your network layout: Very small modifications in the initial layers would lead to very large modifications in the final layers (essentially an unstable computation), so gradient descend simply cannot move that fast.

Instead, it's a vital signal for debugging your network. Inspecting things like gradient magnitudes per layer shows you might have vanishing or exploding gradients. And that has lead to great inventions how to deal with that, such as residual networks and a whole class of normalization methods (such as batch normalization).