You can, but then you run head-first into another problem: this "bar-raising" undermines the legitimacy of the system in the eyes of the people and, not unjustifiably, makes them feel that it is undemocratic. Worse: this is a positive feedback loop. The more you raise the bar, the angrier people get and the more radical they will get in their attempts to tear it down, and so the more bar-raising is needed.
This is the unfortunate paradox that Matthew Yglesias highlighted in "American Democracy is Doomed" [0]: people are raging against horse-trading, organized parties, and 'elites' poo-poohing the "will of the people". This is totally defensible, but to some extent horse-trading and elite rule are the only things that make governance possible. I don't know any solution to this problem.
[0] http://www.vox.com/2015/3/2/8120063/american-democracy-doome...