The manned space program launches from Florida but is controlled from Houston. Why? Wouldn't it make more sense to have both in the same place?

Florida is because there's no other safe place in the US to launch a big rocket on an easterly trajectory* than Florida. Or the extreme southern tip of Texas, which SpaceX uses.

Houston is because NASA needed LBJ's support. They even named the place after him.

* Why easterly? Because that's the direction Earth rotates. If you orbit in that direction you get some free momentum from the planet itself.