They purposely try to spread it around as much as they can to avoid unbalancing the economic and academic equilibrium of the states.

They would save a lot of money by just building everything in one place, say, Texas or New Mexico, but the cost of running NASA, and the academic expertise required to do so would pull so much economic activity, companies, jobs, taxes, and all the knock on effects to that state that local businesses, residents, land values would all spin out of balance, and the states who missed out would have a noticeable dip in business and income tax revenue. They didn't need to build the Saturn 5 first stage in... Wherever, and then ship it all the way down to the Panama canal and back up to Port Canaveral, but they did it to share the load and the economic stimulus.