Horn speakers amplify the sound acoustically, so they require much less electric amplification to provide the same sound pressure. With less electric amplification, you get less distortion of the sound.
Less driver movement
In a horn, the driver movement is only about one fourth for a given sound pressure level compared to the same driver in a conventional speaker box. Driver movement is the biggest source to distortion in a driver, so less movement gives significantly lower distortion.
Small and agile drivers
Horn speakers can also reproduce any given frequency range with much smaller speaker drivers than a box speaker. And with a smaller speaker driver, you also get much faster impulse response and higher breakup modes providing less distortion of the sound.
No distorted reflections
The nature of the horn is to guide the sound into a controlled dispersion pattern, and some designs even do this over a wide bandwidth providing a tool that can direct sound where it is wanted, avoiding reflections off surfaces that distort the direct sound towards the listener.