Basically, if you create a loudspeaker to measure well in an anechoic chamber (the only way you can accurately evaluate its output), it will sound unnatural in a number of ways when placed in a room. Some loudspeakers are designed (e.g., James, Mirage, MBL, Gallo, Ohm) to interact with the room and are the better for it when it comes to natural-sounding listening. But in an anechoic chamber these speakers don't measure so well.
For nearfield monitors, anechoic measurements are valid, but for regular home audio speakers, the *power response* is more important. That is, how linear is the response when it is in a typical listening room, where walls reinforce certain bass frequencies and hard surfaces can make the treble sound unlistenably bright. If you have a narrowed dispersion at the crossover point, this won't be apparent in nearfield listening or anechoic measurement, but will sound thin and hollow at that frequency in a typical room because the narrowed dispersion at that frequency results in less reflection--and therefore less energy--there.
For nearfield monitors, anechoic measurements are valid, but for regular home audio speakers, the *power response* is more important. That is, how linear is the response when it is in a typical listening room, where walls reinforce certain bass frequencies and hard surfaces can make the treble sound unlistenably bright. If you have a narrowed dispersion at the crossover point, this won't be apparent in nearfield listening or anechoic measurement, but will sound thin and hollow at that frequency in a typical room because the narrowed dispersion at that frequency results in less reflection--and therefore less energy--there.