The system of checks and balances refers to the need to ensure that none of the three branches of government is too powerful.
In a representative democracy, the Executive, the Legislative, and the Judiciary must be kept in check by the other two, that is good, although it does not always work. But even if it works it is not good enough because the people can not do the checking and balancing of the three branches.
In a representative democracy, the people have no way of controlling the actual decisions made by any of the three branches.
All the voters can do is wait until the next election; the newly elected may pursue different policies, but they have no less power than those running the country before the election. This means elections do not change the situation.
When the Executive belongs to the same party holding the majority in the Legislature, the government can behave almost like a “dictatorship of the elected”.
As for the judges of the highest court, nobody checks and balances them, unless the politicians directly decide who will be a high court judge. I do not know what is worse; judges without control or judges controlled by the politicians.
The key check and balance any democracy must have is that the people must prevail over the three branches.
Some critics of direct democracy fear “mob rule”. Those who say it do not know direct democracy, or are elitists who do not really believe in democracy or understand it.
In a direct democracy there is no need to fear mob rule because the people follow democratic rules, that is why they have a democracy!
If they do not have those values, they cannot have direct democracy or representative democracy.
The people of stable representative democracies are ready for the transition to direct democracy; their track record proves it.
They have direct democracy in Switzerland. This is why Switzerland is the most stable and most democratic country.
Before adopting direct democracy, Switzerland was also a stable representative democracy for many years. Direct democracy has made Switzerland even more stable.
Switzerland is also a plural country. It has four official languages and four different ethno-cultural communities. Even if the clear majority (60%) of the Swiss are German speaking, they respect the minorities. As democrats, they know it is the right thing to do and the intelligent thing to do. There is no “mob rule” in Switzerland !
The US, and other representative democracies are splendid countries, but until the voters are the final decision-makers, democracy has a way to go.
If you believe the collective will of the majority of voters must prevail over the will of elected politicians, and over the high court judges, then you should push for direct democracy.