With direct democracy you do have tyranny of the majority while this is certainly mitigated in a representative democracy; for instance the 2016 election where the popular vote would have selected a different president.
The US founding fathers were very familiar with Aristotle who stated: "Unlimited democracy is, just like oligarchy, a tyranny spread over a large number of people.”
Indeed the US founding fathers' decisions reflect this, If we're to believe their commentary, they picked a republic with the motivation of liberty for all with emphasis on the elective structure, Constitutional Convention of Hamilton 1787 : "We are now forming a republican government...Real liberty is neither found in despotism or the extremes of democracy, but in moderate governments.”
Scalia has a good talk about this, how a merely constitutionally limited government is completely ineffective of guaranteeing its provisions, its interpretation, and its enforcements: https://www.youtube.com/watch?v=Ggz_gd--UO0
"Every banana republic has a bill of rights"