The all-powerful ability to form cloture in the Senate.
Since the beginning of the Republic, the feature of requiring three-fifths (or at times two-thirds) of the Senate to cut-off debate of a topic has been used for political jockeying and as a legitimate tactic for the minority position to be heard.
While a viable tactic, it has been one that has had mixed results -- sometimes only slowing the inevitable down.Longest Filibusters in the US Senate | InsideGov
Other times, such as Senator Chris Murphy's (D-CT) filibuster trying to convince Republican leaders to allow votes on gun control issues, filibusters work. Republican leaders acquiesced to the demands and conceded to allowing votes to occur.
Sometimes the filibuster is a protest on one's own majority party, as was the case with Ted Cruz's (R-Texas) filibuster that was only supported by 19 fellow Republicans and brought down the anger of the Republican leadership -- anger that would eventually hurt his presidential bid in 2016.
But most often, as in the case of Strom Thurmond's marathon filibuster in 1957, not a single vote changed and the Civil Rights Act passed as written.
The scholarly opinion since the 1990's has been that the threat of filibuster in the Senate has created a de facto super-majority requirement for legislation to become law.
Prior to the 20th century, filibusters weren't as common, largely due to the senator's beholden to the state legislatures and Senate politics were often marked by entrenched state/region-specific issues.
Senators first loyalty was to their state legislatures, then party alliances (often determined by the make-up of the state legislature). Once senators were no longer beholden to the individual states, their first allegiance seems to be their political party, not the voter.
Because of this, factions could form that could gain enough votes to stage a filibuster.
So why doesn't the Senate change the rules, especially when one party controls the Senate with an overwhelming majority?
Almost 20 times during the 20th century, the Democrats had super-majorities in the Senate. They could have changed the rules at any time. Why didn't they?
They did some constant tinkering with the rules, making it easier to break filibusters with a 3/5 vote instead of a 2/3, but the practice was left unscathed.
Simply put, the Democrats knew full well that the tides of politics ebb and flow; eventually, they may be using the same stalling practices.
While Senator Murphy got his way in this most recent filibuster, it's definitely not a given that the other side will cave to demands. In fact, it often strengthens resolves.
The idea of a filibuster is that it is a tool within our system for the minority opinion to be heard. Our country is based on the principle of majority rule, with respect of the minority opinion.
Once the minority opinion no longer has a voice, the entire process just becomes a rubber stamp for the majority's will.
We need the filibuster to remain where it is, a tool to be brought out and used when things need to be slowed down or when bad legislation needs more press coverage.
Because in the end, public opinion of the filibuster is often the only true measure of whether or not it will be effective -- Senate leaders can't ignore public opinion without taking the risk of losing support.