Synthesis DFT Filter Bank
Any spectrum that is between the two DFT bin centers ends up getting represented, in various proportions, in all the DFT bins (in the rectangular window case, the proportions decay as in a Sinc function, roughly by 1/(i-k)).  Those proportions might be needed for your synthesis to be an accurate enough reconstruction.

Using 2 bins alone usually creates a beating effect at a low beat frequency.