Would it be cool if all planets of the same type weren’t a single climate stereotype? Sure. When you’re going to visit multiple tens of different planets in a single play session, does that actually matter? Probably not.

Agreed. Multiple biomes on a single planet would be cool, at the cost of probably an order of magnitude more complexity on the procedural generation engine, but functionally the difference would be trivial when traveling to the other side of the planet to visit the “snow” or “desert” region (if your planet even has one) is about as difficult as just flying to another system with an ice or desert planet.

Can it be done? Probably. Would it be cool? Yes. Would it have a dramatic impact on gameplay? Probably not.