When receiving a modulated signal, what is the adverse consequence of too narrow a receiver bandwidth?

Receiver bandwidth determines how wide a range of frequencies is allowed to pass through the receiver's filters. To perfectly reproduce a modulated signal, the receiver's bandwidth must be at least as wide as the signal's transmitted bandwidth. If the receiver bandwidth is too narrow, it will 'chop off' the outer edges (sidebands) of the incoming signal. Since these sidebands carry the actual modulated data, such as voice audio frequencies, cutting them off results in a loss of information, making the audio sound muffled or completely incomprehensible. While a narrower bandwidth can actually improve the signal-to-noise ratio by cutting out adjacent noise, the primary adverse consequence is losing the vital components of the desired signal itself.