What is an advantage of having a variety of receiver bandwidths from which to select?
Why Noise power reaching the detector is proportional to the receiver's bandwidth, so every extra hertz of passband beyond what the signal needs adds noise and lets in adjacent signals without adding any wanted energy. Setting the IF or DSP filter to roughly the modulation bandwidth (about 500 Hz or less for CW, 2.4 kHz for SSB, 6 to 15 kHz for FM) gives the best signal-to-noise ratio and rejects nearby QRM. Too narrow a filter, on the other hand, clips sidebands and distorts the signal, which is why a selection of bandwidths is useful.
Watch out Power consumption is irrelevant here, and noise figure is a property of the RF front end that filter selection does not change; likewise, a wide filter does not let you demodulate several signals at once in a conventional receiver.
Noise power rises with bandwidth: match the filter to the mode (CW 500 Hz, SSB 2.4 kHz, FM 6-15 kHz).