Consider applying a fixed (time-invariant) filter to each before resynthesizing the signal:
We see that the result is convolved with a windowed version of the impulse response . This is in contrast to the OLA technique where the result gave us a windowed filtered by without the window having any effect on the filter, provided it obeys the COLA constraint and sufficient zero padding is used to avoid time aliasing.
In other words, FBS gives
For these reasons, FFT implementations of FIR filters normally use the Overlap-Add method.