There have been quite a few republics in world history going back as far as 7th century B.C. India. Republics have a lot of adjustable parameters of course, so the name isn’t as meaningful as the form and structure.
Plato’s The Republic was nothing like a representational form of government. Instead two philosopher-kings trained since birth to serve the best interests of the people were made to rule society as dictators. The late philosopher Bertrand Russell called Plato a fascist. It is possible to have republics that are nothing more than claves of oligarchs.
Republics can be regarded as democracy with representatives overcoming the practical problems of distance and other factors that would prevent the majority of people from participating and voting. There is also the problem of occupational specialization such that ordinary citizens cannot spend the time to be well informed on every issue. In the early United States the distance from Washington D.C. of the states meant that all the citizens could not drop their plows off the horse and gallop to vote every day in D.C. before returning home to continue farming. Representative government was a practical adaptation to the challenges facing the designers of the constitution.
Representative government can be co-opted so the practical function is to represent special interests, just the rich or simply socialists in fact if not in law. Inflationary processes can hit a Congress of Representatives too with demographic growth driving up the cost of a campaign run at the office.
I wonder if the United States today has too few representatives per capita to adequately cover constituent opinions and to pay attention to political problems and challenges affecting the nation. Monetary currency is increased quantitatively by the treasury and Federal Reserve from the Bureau of Engraving when more money need be in circulation to serve the population.
The number of U.S. representatives probably should be tripled.