I also have a PhD in Algebraic Topology and feel similarly. One application I'd like to see explored more is the use of differentiable topological invariants as

I also have a PhD in Algebraic Topology and feel similarly. One application I'd like to see explored more is the use of differentiable topological invariants as loss functions for training neural nets. Loss functions to measure topological similarity don't really exist in practice yet and could be very useful.