Would it have been better for Ptolemy to forego the epicycles and suggest that the planets describe simple circles around the earth? Not only would that have been less accurate, but it would have obscured the coincidences that enabled later astronomers like Copernicus to take a god's eye view and notice that a heliocentric framework was a much simpler interpretation of the data.

My point is that complexity was not the problem. If Ptolemy had tried on purpose to make his model less complex, it would likely have come at the expense of accuracy. The problem was that Ptolemy had too much common sense, and was not willing to let the math dictate his physics rather than the other way around.

Considering that, in the end, the Earth does go around the Sun,

I offer this link not as any sort of pedantic correction, but simply as a resource for those interested in learning exactly what modern physics has to say about this question. (Not difficult; highly recommended.)

(An ulterior motive for posting this is that I always have a terrible time tracking down that particular post.)

the Earth does go around the Sun

And the Sun does go around the Earth.

Of course, most of the observation that led to people thinking that the Sun goes around the Earth in the first place was based on the Earth's rotation on its axis, so that's a whole different issue.