Did read through stackexchange. It is indeed complicated. But the top response feels like paralysis by analysis. If we analyzed turbulent flow too much we would be unable to build rockets. Remember frictionless planes and point masses in high school? Those results are not exact either but a great way to model and understand what is going on.
Soooo .. could we make simplifying assumptions here? What if the earth was a smooth rigid sphere with a layer of water on the surface? The center of mass of Earth-Moon is at ~3/4ths of the earth's radius, from the earth's center. They are rotating about that center. The 12+ hour tides in many parts of the world start to make sense. Is there a mistake in this mental model?