Some individual rights need to be protected against the "tyranny of the majority." For example, a person with an unpopular view should still enjoy free speech. And of course, a majority should not be allowed to vote to enslave a minority.
That's a great argument for the 1st and 13th amendments. Perhaps those should actually be written in to the new document itself. We could even go further and adopt the Universal Declaration of Human Rights.
That doesn't change the fact that the American three branch bicameral system has not aged well and is profoundly undemocratic by design.