Because you vote for somebody who says he will fix something doesn't mean he will... they need to be held accountable somehow... Obama is an example of this.
In direct democracy, you either have populist votes or non-participation. It is inescapable.
The fact that the current system is broken is no excuse to move to one that is flawed from the start. We now have the technological means for an evolution of representative democracy: Liquid Democracy, or delegative democracy. It's representative democracy with "continuous elections". It might work (better).
And the Uk PM or Home Secretary would have sorted out the problems you have with over mighty small town police forces very quickly.