To be honest I think your explanation misses the point in two important ways.

First, the Fourier transform does not just measure the 'energy' or amplitude of a single wave; it must also take into account its phase.

Second, complex exponentials are in no way an essential ingredient for defining the Fourier transform. We just work with them for computational simplicity, essentially because exp(ix) exp(iy) = exp(i(x+y)).

I also have trouble assigning meaning to your last paragraph. After all, complex exponentials can cancel just as much as sine waves (proof: sine waves are a combination of complex exponentials).