Purpose of Dome on Tweeter...

It depends on how the tweeter is designed. A lot of tweeter models will use the dome (dust cap) for dispersion. It also keeps dust and dirt out of the voice coil and motor assembly.

I get a chuckle out of some ads that have all of the dust caps pushed in and the owner states; "this doesn't affect the sound at all". Yeah, right.

Tweeters come in many types: Cone,Dome,Horn,Ribbon,Electrostatic,etc.
Why would the factory push in the Dome?
Would you buy a watch with no lens?
Like Mofi states,it's the design.

The dome of a dome tweeter is the diaphragm, the part that moves the air to create high frequency sound. It is driven by current moving through the voice coil which is in contact with the dome just behind it. Without the dome in place the voice coil itself would not be effective at moving enough air to make the sound level audible. The shape of the dome does affect its dispersion, so having a dent in it will affect its performance to some degree. There are soft and hard dome designs, and neither operates ideally as a perfect piston. At certain frequencies the dome will resonate, and its shape is important at those frequencies since breakup modes occur.

If not, why aren't they just pushed in at the factory?

That would be the inverted dome tweeter like Wilson Audio uses.

"03-13-15: Tls49

If not, why aren't they just pushed in at the factory?

That would be the inverted dome tweeter like Wilson Audio uses."

Its only inverted because they installed the tweeter backwards. Its a quality control issue.