Why does a dent to a tweeter not affect sound quality?

This is an excellent question. I had a pair of Celestion Kingstons whose aluminum dome tweeters were exposed. Two nephews visited and damaged the tweeters, one much worse than the other. I was pretty heartbroken, because Celestion was out of business by then. I waited a couple of months before I had the heart to listen to them, and surprise, I couldn't hear a difference. 
Had them for years after that, not using them and trying to sell them with no luck. I finally found an interested party, a British gent who had connections with one of the speakers designers in Ipswich and could have it repaired. He had previously owned a pair of them for years and knew them well. When he got them home, he emailed me and said that he couldn't believe that they sounded fine to him, just as I had told him.
Yes, you would think that a badly damaged metal dome would sound terrible, but apparently that's not always the case.  

I have pair of JBL 4311's with one tweeter with a slight dimple. and one that does have a side push. You know what? They sound fine. And they will bring $400-$600 just the way they are.

This all depends on what speakers, and the severity of the dent.

It is mainly for protection and air leaks. When the cone is modified a phase plug either fixed to the cone or stationary can be used. There is a place for weezer tech too.

Very interesting phase plug tech, I use it. Mine are stationary.
The cone bore vs phase plug gap is very important (air leaks cause noise) Phase plug length and the tip configuration is # 1 in mechanical distortion control for any inverted cone driver

I always thought domes in the center of a cone were for the the sound waves coming back on the cone. Just like covering the WHOLE surface with a dome. Its not so much for the waves going OUT but more so for what’s coming back. That is where the measurements will get wiggy if they are crunched.

As far as fixing domes I’ve fixed hard domes that have cracked and soft domes (or rings) that were torn. Nail polish makes quick work of that problem. A few strands of insulation fiberglass and cover the crack.

DENTS pull them out with tape and if they are bad use a sharp dental pick (or two) and if you manage to poke a hole, a little dab will do ya, of what ever you like.. Nail polish to Flex Seal, it ALL works fine.

I repaired 2 different set of QLS1s. I got pretty good at fixing some weird ones.. I think they were ringed mids. 20 + years ago. That was a great speaker Infinity QLS1 Ribbons and domes.. The wires would delaminate from the domes and of course 50% were smashed in and a few 10 penny nail holes. I think they are still in service. Surrounds 4-5 times. They had a servo model too.. These weren't

Wait when weezers come back they will be all the rage, how to add a weezer to your speaker.. :-)

Regards

My ears are not good enough to tell, but it can be measured. Are you talking about whizzer cones, oldhvy?

Yep fiesta75, that's them all right. They look weird but they sure work.
I used 12" Eminence 103 E in a Mids column not Mid Bass mids..
2500 hz and down, that weezer sure helped with the beaming.

 Using a 12" at that high of frequency have glaring mids. A lot better dispersal pattern and smoothed everything right out.. 
Helped with cone break up too.
A Weezer cone. Yup.

I gotta finish that project come to think of it.

Pioneer made a very popular one too 51/2 or 61/2 with a weezer. A lot of the old boxes used that driver or copied it.. Great driver.

I'm pretty sure Tannoy Concentrix drivers used them.. Seas..