This is because there are other (importantly) significantly less internally destabilizing ways to remove the threat of democracy, and the institutional structure that (nearly) enforces the two party system is just one example. Soft media control is another - a politician like Sarko isn't getting elected in left-leaning country like France without it.

The American public is significantly to the left of both parties. We don't get to vote on the military budget, for example, and for good reason - if you poll people that identify as republican and ask what % of their tax dollars should go to the military, you're going to get an average number that is far beneath current allocation (around 50%). When it comes to education budgets, though, voting is most definitely allowed - growing school districts generally have to resort to bond measures to build schools, and by law, they can only be approved by a public vote.

If you can convince the public that voting is the highest socially acceptable level of civic participation, as this country has done with its citizens, cynicism and resignation are the inevitable result when staring up at those static, elite controlled institutions.

you are the media you consume.