I believe to take a gap year or not should entirely be up to the individual, some may want to get started immediately after high school while others may need a year off to mature more before being able to seriously tackle college, but overall I think it would be a poor idea to require a gap year.
Not all options for students are equally beneficial. Some students do well after a year off. Others enjoy keeping to the rhythm that they have had their entire life. Leaving this decision to students and their parents is a much better plan than requiring students to take a year off and they possibly lose interest.
Colleges should not require students to take a gap year before attending school. This is because of the fact that many students take math classes that segue into more advanced math classes. Taking a year off of school due to a mandatory gap would only interrupt and possibly damage the learning experience.
I do not believe that college students should be required to have to take a gap year before attending school. I think that it is unnecessary for them to wait a whole year before they can go to college. A lot of people want to get college over with as soon as possible.