If a time-domain signal has sharp corners, its frequency spectrum will contain high-frequency components. Truncating the spectrum results in Gibbs' phenomenon. So if you're trying to design an FIR, you really want the target frequency response to be nice and smooth so that windowing the impulse response down to a finite length doesn't distort the frequency response too much.
Currently I'm contemplating trying to design a very strange filter: One that has unit gain at all frequencies, but non-zero phase. I'm wondering whether or not a similar phenomenon occurs: If the filter has unit gain at all frequencies, then what does truncating the impulse response do to the phase alignment?