I think autodiff is mostly interesting because of optimization by gradient descent, and gradient descent is only efficient using reverse-mode autodiff, which can't be done with dual numbers.

I think optimization by gradient descent (and its variants like Adam) is interesting because it's the only optimization algorithm family I know of whose runtime scales linearly oreven near-linearly with the number of dimensions, so for large-dimensionality problems it's the only computationally feasible algorithm. Also, though it's only guaranteed to find the optimum for differentiable convex problems, in practice it seems to work well enough to be interesting for nonconvex problems.

I think optimization is interesting because it allows you to solve arbitrary inverse problems, or at least continuous relaxations of them.