But that's exactly how it is now.
I personally like the verified user option but I can understand how some wouldn't for reasons like the one you give. Frankly, I think Twitter's focus on growth is a big part of what got it into this problem in the first place. I'd rather see them focus on quality than growth and I think expanding the verified user program does that.
The measure-of-connectedness option is a little gentler and would probably fix a pretty big piece of the problem.
Quality of what? Discourse? Network connectedness? Ad-accuracy? (I'm nitpicking, but I'm curious what you mean.)
So the logical next question is how does Twitter shape how it is used? I think the answer to that is in part, let other people take care of that. In some ways, Twitter-the-platform is much more interesting that Twitter-the-product. My current favorite example is Nuzzle.
Unfortunately, Twitter is a $13 billion (and falling!) company. Investors think Twitter is Facebook Jr. and it really isn't.