Super Mario 3D World theory

Rosalina was kidnapped by Bowser and he used her power to take over the Mushroom Kingdom. So the reason you are catching Green Stars on your way is so you can unlock certain levels to go through. The worlds don't have full themes but do have small things that connect each level. (One world has a lot of larger levels, one has more upward levels, etc.).

So the reason why Peach isn't kidnapped and why there are Green Stars is possible explained.