"States" are a fiction. There are only people. So to translate what you wrote into on-the-ground reality: the senate exists to make sure that the people who live in states with small populations are not subject to the will of the majority of people in the country.
This is defensible, and I'm sure you would not balk at being called "anti-majoritarian", but lets be clear about what is going on.
Also, post-Civil War, this "we're a republic not a democracy" stuff really changed significantly. While it may have been absolutely true in 1776, it became much less true in the 1800s, and has continued to become even less so in the 1900s. It may have been better if the Constitution had been amended to reflect this (since it was happening anyway), but it's burying your head in the sand to pretend that the original conception is reality on the ground today.
