No, not like this:
Hear me out!
As Stack Overflow grows, it becomes increasingly ridden with extremely newbie and mediocre questions. It's just natural. The team are fighting hard to keep the crap out, but there are many very basic questions that are okay on their own. They don't deserve to be kicked out* - they are just very, very, very basic and/or localized.
Too much basicness tires users who are interested in discussing more advanced topics.
As has been discussed many times over, the voting system is not suited to identify advanced questions due to what is known as the bike shed effect. A group of people will vote on what they understand, which puts truly expert questions at a natural disadvantage that a democratic voting system can't overcome.
Now, there is a small number of users on Stack Overflow who I, as a user, know share my basic values (like, teaching a man to fish rather than fishing for them); I also know they are experts in their fields. It is safe to assume that what these users regard an interesting question worthy of attention, is likely to be interesting to me as well.
The idea is to introduce an opt-in "follow" mechanism that allows followed users to share what they find interesting, with very little fuss and on a purely opt-in basis.
Allow every SO user to follow any other SO user with a certain minimum rep, say 3000.
To every user who is being followed (or every user), display a new link underneath every question, "Recommend".
Introduce a new filtered view somewhere, named "Recommended". The view will show me all questions that my followed users are recommending.
Whenever I browse a list of questions, highlight those questions that have been recommended by my followed users. (I haven't put much thought into how to implement this graphically - you get the drift.)
I'm not especially fond of social networking, and I think most of it doesn't have a place on SO. But I'm starting to think this specific thing could be the right way to go in order to tell apart expert content from the 10000th dreary "how do I upload a file" question.
This is an entirely opt-in feature - unless I actively follow some users, I will never notice this.
Maybe for a bit of ego-stroking, the profile page can show how many users follow you. Or even who. Everything else would simply be kept under wraps - no publication of follower data in the data dump, no follower leagues or anything like that.
* At least not under current SO rules. Maybe those rules need to be changed - but that is a different discussion.