That's a direct democracy.
The Roman Republic didn't protect individual rights. It protected the right of the elites to rule the City, without interference from the headcount. Senators had to campaign for election, but only the wealthy elites were allowed to run for the Senate or given religious leadership.
The original Constitution only protected the rights of white male land owners, despite its high minded language. The nuts and bolts of the founding documents only gave individual rights to land owning white males. The Founders created a system to amend the constitution to allow government to adapt to modern conditions, but the US has done little to update the document and it is now woefully out of date.
Now, instead of bringing your Constitution into the 21st century, Republicans want to go back to the original intentions of the Founding Fathers. A bunch of 18th Century rich men who lived in an agrarian coastal nation of about 4 million people in a time when guns were single shot muskets, communications took days and weeks and there was no mass anything.
In the late 1970's Pierre Elliott Trudeau, wrote our current Canadian Constitution. The original Canadian Constitution was an act of the British Parliament in 1867. While at the time, the new Constitution seemed like a PET vanity project, it made Canadians think about what kind of nation we want, and how to achieve it and it established a wonderful framework upon which our nation is building. It was a national self-esteem boost which has never worn off.