The other significant reason for putting a spaceport further south is the inclination of the orbit (angle of the orbital plane to the equator) is limited by the latitude of the launch site (without a secondary maneuver after launch). So for example if you launch due east (which gives the most advantage of the Earth's rotation) from Cape Canaveral, which is at a latitude of ~28 degrees, you will end up in an orbit with a 28 degree inclination. Launching further North or south you end up with a higher inclination either way. So in order to get an inclination close to equatorial it is easiest to launch closer to the equator. Its a bit hard to visualize but this article has some good explanations [0].
The other significant reason for putting a spaceport further south is the inclination of the orbit (angle of the orbital plane to the equator) is limited by the latitude of the launch site (without a secondary maneuver after launch). So for example if you launch due east (which gives the most advantage of the Earth's rotation) from Cape Canaveral, which is at a latitude of ~28 degrees, you will end up in an orbit with a 28 degree inclination. Launching further North or south you end up with a higher inclination either way. So in order to get an inclination close to equatorial it is easiest to launch closer to the equator. Its a bit hard to visualize but this article has some good explanations [0].
[0] https://www.planetary.org/articles/3450