Speakers sound better without grilles?

Depends on the speakers, but certainly many speakers do sound better without their grilles. Some manufacturers explicitly recommend removing the grilles for serious listening. Others (e.g., Paradigm) design their grilles to actually enhance dispersion - my Paradigms definitely sound better with the grilles in place. For most speakers, grilles are just for appearance.

LS3/5a's are supposed to be listened to with the grills on since it was designed that way. Some cannot tolerate listening to speakers with the grills on and invariably will remove it due to habit irrespective of what the speaker builder says.

It is rare that a speaker sounds better with the grills on. One exception was a pair of NEAR model 10M I believe; the grills actually tamed the harsh metal tweeter.

My experience has been just the opposite of Xiekithen's. I've owned quite a few different speakers and have only found a couple that sound better with grills removed and they were specifically designed to be used sans grills. Meadowlark Kestrels and Sheawaters are what I'm referring to. I owned NHT Super Ones and SB-3s and the SB-3s definitely sounded better with grills on, never tried the Super Ones without grills. I've also tried Acoustic Energy speakers which were recommended to be used sans grills for critical listening but I preferred the sound with grills in place. All of this is a matter of taste I suppose.