These techniques have already been used to solve problems using DNA computing [1]. Digital circuits don't solve anything either, they are just electrons flowing around mediated by semiconductors after all and the results of their computation are just measurements of electrical charge values after those physical systems have had time to flow around. As long as you can set the input and get a consistent output and measure that output you can compute with it.

To use your logic: Large integrated circuits take an enormous amount of computing power to simulate correctly. But integrated circuits aren't smart, they just do what integrated circuits do.

[1]https://en.m.wikipedia.org/wiki/DNA_computing