Metal tweeters may be brighter and some harsh but they are also generally speaking able to produce finer detail and handle more power. If your mounting your speakers low in the doors the brightness may be beneficial as well.
1) No, metal tweeters tend to overemphasize certain notes due to "ringing". Think about hitting a bell. It continues to vibrate
after you hit it. The silk tweeter has better damping, or a lower "q", and adds less to the music.
2) It's possible that a metal tweeter radiates heat a bit better, but neither enjoys much of a benefit in power handling.
3) With a 1" diaphragm, it is much easier to get a silk dome to have a lower mechanical resonance - you can get it to play lower and still sound good. Since cone mids have worse off-axis dispersion the higher they go, lower-playing tweeters are important for door mounting (less so for on-axis mounting - kicks and home speaks).
This is why Dynaudio, Morel, DLS, Rainbow, Alpine/Scan-Speak, Phass/Scan, a/d/s/, etc., all use silk.
4) Over time the harsher ringing at the bottom of the range (the upper mids/lower treble) becomes tiring and contributes to listener fatigue. I have MBQ with the Musicomps in my Honda, and I have the Alpine/Scan-Speak in the Acura. After listening to the Acura, I can hardly listen to music in the Honda for more than 20 minutes without starting to hate those titanium tweets, and they are low in the door, too.