The geocentric interpretation was largely forced due to religious dogma and not due to a belief that it was simpler. It's honestly crazy how close people 2000 years ago were to a more contemporary understanding of the universe and how all that became lost and suppressed for ~1500 years.
[1] https://en.wikipedia.org/wiki/Aristarchus_of_Samos?&useskin=...
[2] https://en.wikipedia.org/wiki/Seleucus_of_Seleucia?&useskin=...
If Earth orbits around the sun, you'd expect we'd see the stars move, as Earth moves relative to them. You have to assume the stars are absurdly far away to make that model fit with observations.
Of course, now we know that stars are that far away, but I can't fault the Geocentrics of old for picking the more reasonable model.