Actually, no - Trump is the proof that democracy does work.

 Firstly, US democracy was designed with a situation in mind that a completely random person can become a president - that's what's built in. It happened, like it or not.

 Secondly, US democracy was designed so that even in a situation when a completely random person becomes a president, there are still checks and balances regarding the damage he can do. So far, Trump's rule was very short on outrageously stupid decisions of meaningful impact, even if there are plenty of not widely popular decisions made.

 Thirdly, even with Trump at helm, you can be certain that there'll be an election in four years where Trump can be unseated, and in eight years Trump will be gone.