This is probably a dumb question but here it goes:
Variational Quantum Algorithms (VQAs) are the leading proposal to derive quantum advantage use NISQ devices. VQAs employ classical optimization algorithms as part of the VQA algorithm.
Classical optimization algorithms can be very expensive to implement for quantum mechanical problems. For example, the Hamiltonian matrix has size that scales exponentially with the number of qubits. So how can we really derive quantum advantage in this case if the underlying classical optimization problem is hard to solve to begin with?