The type with a circular area very near the surface of the tweet dome are 'phase plugs'. They usually are there to create a wider dispersion field for the tweeter, at the cost of clarity of the direct sound.
I had them on my Canton CD300/Cd360 speakers (for my 5.1 setup) and remove all of them fronts. center, and surround) taking them off MY Cantons helped the sound be clearer.
I would say they are a tradeoff put on 'lesser' speaker tweeters to accomplish something a different design would do better at.
For the rest of the designs for tweet covers that are just bars or a screen, they ARE just to protect the tweet dome from kiddy hands, and drunken guests. And those can also be removed to better effect with the hazard of squishing the dome (Which I have done on my B&W 805S in a drunken stupor, New Years Eve...)