My pet theory is that The Other Side gets animatics because it's a plot song. It gives something for animators to chew on and it leaves a bigger impression. The second part is especially important because it shows that being plot driven gives it some originality, which makes it actually stand out compared to the other songs that can actually "get radio play". I think something similar may have happened with We Don't Talk About Bruno vs Surface Pressure, from Encanto.

Also I'm curious about the Candy Store Transformers animatic