Correct. However one of the key differences is that when the Republic was established, per the Constitution, States' Rights were a primary aspect of legislation. The federal government had very little power and very few laws compared to today. Most laws existed on a state-by-state basis. The USA of the late 1700s was really more like the EU than it is today.

And that's why New Hampshire needed senators. New Hampshire needed to ensure that it could still get the things it needed from the federal government (presumably money in most cases) to make New Hampshire a good place to live. That's why land has voting rights -- New Hampshire (using it as an example for all less-populated rural states) used to be a lot more sovereign.

Now things have changed. New Hampshire isn't just ensuring that it gets the resources it needs. Because most laws in the US are now enacted on a federal level, New Hampshire is deciding implicitly how /other/ states behave. And this is the problem, and is clearly against the intent of the Constitution ("any power not explicitly granted to the federal government will be left to the states").

So, the bicameral legislature as designed made sense. But in its current context, it's fundamentally broken. If we want to return it back to its original intent, then it's time to get back to a period of States' Rights.