"There's a reason they are the minority - because their policies do not reflect the current desires of the majority of the constituency."
That's the problem, though -- that's not true. Senators are elected for six years, and early in their terms, they can be pretty forgetful of their constituencies. The point of having a filibuster, but making it dramatic, is exactly that: make it so the minority party can use it, _but if they use it in an unpopular way, they will get shellacked_.
The most famous recent example of this, you probably _won't_ appreciate, at least in a partisan way, but hopefully you can at least in an objective way. In 1993 the GOP filibustered the Clinton health care plan (technically they never had to -- it was so clear they would that it was never brought to the floor). The Democrats would likely have had the votes to pass it otherwise. In the '94 midterms, the populace overwhelmingly endorsed the GOP's blocking the bill (among other things) by giving them large majorities in both houses of Congress.
Hillarycare was extremely unpopular, but would likely have been forced through anyway, absent the filibuster.
Another case, probably closer to your heart although less clearly enforcing the will of the people, was GW Bush's judges.
Well, I don't have a better list of examples to hand, sorry (there doubtless are some), but anyway, I think it's an important tool to enforce more deliberation and consensus. As I say, I think it should be made harder to do, in the sense that you should actually have to slow down the Senate and take possible public heat. Right now it's evolved into basically a rule where 60 votes are needed to pass anything. It should be more of a "the minority can choose a couple things a year on which to go down fighting if they're sure the country is behind them" sort of thing.