It's actually less about symmetry than it is about underlying criteria.
I think I used a term which you did not appreciate the meaning of, for which I apologise. Let me explain.
"Symmetry" in science means "let's take these unconnected things and arrange them so that patterns form." This is exactly what you have done: you've taken seven types of planets, arranged them so that a pattern forms, and then added another one to complete the pattern.
The gobi and antarctic are also deserts. The description of a desert world would mention that it has cold polar regions. Desert is about dryness with both extremes in temperature. Savanna worlds are hot and dry
I understand the meteorological definition of a desert. However, this is not a game about scientific rigour. (It features planets orbiting O-class stars, after all.) This is a game which sacrifices rigour for "what feels right." To most people, what feels right meteorologically is that deserts are hot places full of sand and baked rock.
If your desert planets are not like this then people will be disappointed, because they wanted Tattoine and you didn't give it to them.
Yes, a concern is too many cold types. Glacial description would include mentions of global oceans and equatorial wetlands, Ice would have smaller oceans, and tundra would have deserts.
This brings up another common problem in game design: flavour text is not a bandaid. If your system is unintuitive then you can't use flavour text to fix it, you need to go back and change that system so that it becomes intuitive.
Interestingly, World of Warcraft has done studies on flavour text (don't ask me how) and has confirmed that most players like having it there but don't even glance at it. It could be lorem ipsum for all they care.
Yes, this is sort of going to be an issue. In MoO2 for example, aquatic races loved pretty much any planet with an ocean and it was a powerful perk. The idea here is that the wetland planet has more water coverage and the glacial planet has more floating ice in it's oceans, and the people from the ocean planet might be used to living in the polar regions.
Aquatic subterranean was a fun combo. Wow, remembering back, MoO2 was fun. I should play it again.
Forget about Gaia on the grid. It's a circle of 8. You can put Gaia on the center and note that everyone likes it.
Then why bother having the grid at all, if not every spot is filled?
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