The US is a constitutional republic, which functions through the process of representative democracy.
This is the same thing they are pushing for in Iraq. They call it democracy because that is the word most people understand and recognize and it
conveys the basic principle quite well.
en.wikipedia.org...
A constitutional republic is a state where the head of state and other officials are representatives of the people and must govern according to
existing constitutional law that limits the government's power over citizens.
And here is a blurb from Wiki about the reasons for checks and balances and a constitution even within the seemingly fair democratic process.
en.wikipedia.org...
There are several varieties of democracy, some of which provide better representation and more freedoms for their citizens than others.[7][8] However,
if any democracy is not carefully legislated – through the use of balances – to avoid an uneven distribution of political power, such as the
separation of powers, then a branch of the system of rule could accumulate power and become harmful to the democracy itself.[9][10][11]
The "majority rule" is often described as a characteristic feature of democracy, but without responsible government or constitutional protections of
individual liberties from democratic power, it is possible for dissenting individuals to be oppressed by the "tyranny of the majority". An essential
process in representative democracies is competitive elections that are fair both substantively[12] and procedurally.[13] Furthermore, freedom of
political expression, freedom of speech, and freedom of the press are essential so that citizens are informed and able to vote in their personal
interests.[14][15]