How much can I change the height of a cake?
I have found that, for most cakes, variations in the height of the layers doesn't cause any problems. As you noted, you need to keep any eye on them for proper doneness. If the layers are substantially thicker you may need to slightly decrease your oven temperature to ensure proper doneness without drying the cake out.

I use the same batters regardless of the size of the pan or thickness I am looking for. I have 7, 8, 9, &amp; 10 inch cake pans and I regularly vary the diameter and/or thickness of the layers depending on the end result I am looking for, how I want to present the cake, etc.

Regarding my remark about most cakes, there are exceptions. For most cakes, I want a moist cake that doesn't crumble when cut or eaten. Variations don't hurt these layers.

However, I use a different batter when making super thin layers (10 - 12 layers will result in a 4" to 5" tall cake).  This batter results in a dryer texture which works well because they get some moisture from the frosting. Being so thin, the level of moisture works out very well. If the layers were moist to start with, the cake would turn to mush. You wouldn't use this batter for any normally thick layers, cupcakes, etc. as it will crumble terribly.

Hope this helps. And, just an observation here (could be my imagination), but it seems like people think thin layers are more special. Maybe they think you put more work into it
or maybe it's just that it's more unusual these days to see thin layers.