Why do more phase shifts cause the need for higher bandwidth when Frequency Shift Keying (FSK) is used?
I believe you mean a discontinuous phase when switching between two symbols. If the phase jumps at the border between two symbols, your modulated signal is discontinuous. This means that it contains many (theoretically all) frequencies, so it has a large bandwidth. On the other hand, if you always have a continuous phase, there are no discontinuities in the modulated signal, which requires much less bandwidth. Note that the smoother a time-domain signal is, the smaller is its high-frequency content. FSK with a continuous phase is called (what else?) continuous phase FSK (CPFSK). It is a special case of continuous phase modulation (CPM). Also check this link.