What is the effect of wiping the right half of Fourier Transform bins?
The discrete Fourier transform (DFT) transforms a sequence of generally complex-valued numbers to another sequence of generally complex-valued numbers. If the input to the DFT is real-valued - as is the case for a sampled audio signal - then the right half of the DFT is redundant. If $X[k]$ is the length $N$ DFT of a real-valued length $N$ sequence $x[n]$, the following holds:
$$X[k]=X^*[N-k],\qquad k=0,1,\ldots, N-1\tag{1}$$
where $^*$ denotes complex conjugation.
For even $N$, the values $X[0],X[1],\ldots,X[N/2]$ completely represent the original sequence $x[n]$, so the DFT coefficients $X[N/2+1],\ldots,X[N-1]$ can be discarded. For odd $N$, the coefficients $X[0],\ldots,X[(N-1)/2]$ are sufficient.
Note that there are efficient routines for computing the DFT of real-valued input sequences, which only compute the non-redundant DFT coefficients.