You see the problem yourself by pointing out the required increase in computational capacity. Quantum mechanics can be described and predicted using fairly straight forward mathematics. Its
descriptive complexity is lower than for a cancer whose functioning is a non-linear dynamical system not at thermodynamic equilibrium and changes in time. It's true that for QM, the computational complexity quickly goes up beyond toy harmonic oscillator problems but in a search for a theory, the descriptive complexity and number of fundamental parameters per observation is what controls search time.
We also don't know to what extent quantum computation would aid predictive modeling of protein interactions. It's possible that there are no leaks at the classical level of abstraction as to hurt predictability. But the problem still remains that experiments to fix parameters are hurt by the fact that the system is changing under you and interacts in a complex way with its environment which can't be known ahead of time. So the computational complexity is not necessarily easier (in a practical sense) even if we assume that there is no utility in modeling quantum effects.
One very theoretical idea of solving cancer (per cancer) would involve searching for a 'problem', an insult, outside of the learnability class of evolution which also does not harm healthy cells. This is computationally likely harder than BQP. Anything less, even if equipped with a quantum computer, would be evolved out of and with any survivors less attackable. Any way you look at it, it is a far harder problem than working out fission.