A sfar as we know, the problem of solving the Schrodinger equation would be exponentially faster on a quantum computer than the fastest possible non-quantum computer. Given that "neuromorphic" computers are classical computers, we don't know of any way to achieve a similar speedup for this problem, so we can at least say that there are applications for which we need a QC if we want to solve them. Of course, it's possible that those are far fewer than "neuromorphic" computers, so it may make more sense to invest more in the latter.

Note that I'm putting neuromorphic in quotes because it's mostly a marketing term, the resemblance between memirstors and neurons is at best symbolic.