I agree with you, but with a couple of corrections. The cheaper algorithm called Density Functional Theory is probably the most popular kind of quantum calculat

I agree with you, but with a couple of corrections. The cheaper algorithm called Density Functional Theory is probably the most popular kind of quantum calculation on molecules, and scales as ~N^2.5 in practice. On the other hand, the number of basis functions is a more than the number of valence electrons in the molecule (if the calculation is at all sane), much larger than the number of atoms. So the exponent is often smaller than you said, but the N is also much bigger. So in the end you're absolutely right about the need for quantum computing for molecules.