Using (Ptolemy's) basic model approach (same as Hipparchus) he successfully developed a predictive model that fit the observations available. He did not have any data that disputed that the Earth could be at the center of the system.

I'm not sure we should continue this discussion in this thread, because we're getting quite far from the original subject. But I certainly agree with both of those statements.

Choosing an Aristarchian heliocentric model was an option, but there was no actual reason for preferring it.

Well, no, there was indeed a reason, but Ptolemy didn't see it. If he had started with the assumption that Earth orbits the Sun and then -- unlike Aristarchus -- actually sat down and done all the math, he would have realized that the heliocentric model is mathematically much simpler and more elegant, and allows much faster computations.

That is precisely what Copernicus did, and when his book was published everybody who was anybody instantly realized that Copernicus's model was much less cumbersome. So even astronomers who fervently believed that Copernicus's model was false used it for practical computations.

Tycho's model is computationally identical to Copernicus's but allows a stationary Earth. In that model the Sun orbits Earth and all the other planets orbit the Sun.

Ptolemy's model was unnecessarily complex because he introduced one epicycle per planet to account for retrograde motion. In Copernicus's and Tycho's model, one cycle -- Earth's orbit around the Sun or vice versa -- does the work that Ptolemy needed five to accomplish.

The other major false assumption in Ptolemy's model -- one that was deeply rooted in the Greek worldview -- was that all celestial motion is necessarily circular and at uniform speed. Kepler's laws, which show that planets move at non-uniform speeds on elliptical orbits, were truly revolutionary. Not a single astronomer before Kepler thought to challenge the assumption of uniform circular motion.