I have come to realize that my beliefs are very similar to the beliefs of the university
What beliefs? Specify on how you connect with Columbia. Talk about your shared ideals, that will make it more specific to the prompt.
As a person who has a wide range of interests and wants to put his hand in multiple buckets
Again, try to be more specific. What interests do you have and how can Columbia excite your intellectual curiosity? You talked about the Core Curriculum, which is good. However, don't shy away from mentioning some of the classes that you're excited to take within this Core. It'll show the admissions officers that you've done your research instead of making general statements that can apply to any school.
Hope these suggestions helped!