The problem is that the "constitution is a living document" concept is very much scorned by traditionalists in general. They don't want things being reinterpreted in light of current situations, they want the law to remain static and they don't want our society to progress because (for various reasons) they believe it isn't necessary and would be moving away from the model of success that got the United States where it is today.
I agree somewhat, there's certainly something to be said for a lot of the rights and privileges that we extend to citizens. We have created our own success to a certain degree, but when you look at history, it's fairly evident we've gotten lucky and used underhanded tactics to get what we want at times too. It certainly helps that over the course of our history, we've acquired a ridiculous amount of territory to expand into while other colonial empires shrank in influence and landmass. Our exploitation of Indians in stealing their land, Africans as slaves, and South Americans in the early 20th century surely played a part in our amassing of wealth and affluence.
The Traditionalist mindset envisions some Golden Age of America that existed in the vague 'before,' idolizes the Founders, and glosses over all of the sins of our past, arguing that instead of progress we need only harness the things that made us great before. They've revised history to blot out the Imperialist ambitions America acted upon, to marginalize racism, and even glorify the revolution that founded this country (forgetting that George Washington started the French and Indian War by invading the Ohio River Valley with other settlers, which eventually led to the taxes we revolted over). Our past is not pristine, but that doesn't mean that the Constitution is not without its merits.
The biggest problem I see is that "legislation from the bench" by interpretive justice (as I like to call it) is disconnected from the Democratic process. Decisions reached by the Supreme Court are completely insulated, to the point that the Justices often do things that the majority of the American people disagree with. These initiatives, pushed forth by unelected individuals, become sticking points and controversies in American Society which are almost unresolvable. I would go so far as to say that they play a very large part in the political divisiveness that has manifested itself in our politics in a very extreme fashion.
Once something is mandated, essentially, by the will of the Justices (sure, it's based on logic, but ultimately it is their opinion) there is no going against it in a practical sense. Sure, there are constitutional procedures for dealing with it, but it's far too impractical in our society to actually employ any of them (I believe they were set up for a much smaller nation). The only way to have the decision overturned is to wait, change the make up of the court, and hope that the right people are nominated into the position (which again is out of the hands of the people). Meanwhile, American Society rages back and forth over the issue and it becomes a hotbed of disagreement, anger, and resentment--just take a look at Abortion. It probably would've been resolved awhile ago if it wasn't a Supreme Court based pronouncement. Gay Marriage is shaping up to be the next issue, which I think will only serve to extend the life of the controversy long term instead of resolving anything.
To me, the solution is extremely obvious. If you want the Supreme Court to have any accountability so that people actually pay attention to what they do, they need to be elected officials. Our system of government was designed by people who had little faith in the public on the whole (think Electoral College and the way they described Democracy as Mob Rule), some things need to change. Lifetime terms make it impossible to remove judges that show poor judgment (not that we'd see as it is, their secretive nature defeats any transparency there, and that needs to change too), so we would need to switch to 8, 10, or 12 year terms.
I agree there's a great deal of detachment from politics in our society, and there are even more people who have strong opinions, loud voices, and are wholly uneducated about the facts surrounding the issues. Recognizing that problem, you can do one of two things: take power away from the people and trust that whoever you do give it to will exercise it better, or give the people more power and hope that the weight of that responsibility wakes them up from their apathetic trance. I think I'd prefer to go with the latter, because it's almost never employed, and far more just.
There are those who say people as a whole aren't capable of rising to the occasion, and I think it was Noam Chomsky who had the best rebuttal to that (though I don't necessarily agree with the indoctrination angle as much as the comments on wasted intellectual potential):
Take, say, sports -- that's another crucial example of the indoctrination system, in my view. For one thing because it -- you know, it offers people something to pay attention to that's of no importance. [audience laughs] That keeps them from worrying about -- [applause] keeps them from worrying about things that matter to their lives that they might have some idea of doing something about. And in fact it's striking to see the intelligence that's used by ordinary people in [discussions of] sports [as opposed to political and social issues]. I mean, you listen to radio stations where people call in -- they have the most exotic information [more laughter] and understanding about all kind of arcane issues. And the press undoubtedly does a lot with this.