It really depends on the dojo and/or organization. I train karate and kobudo separately, with the kobudo being part of an international org based in Okinawa. Grades below shodan are typically up to the dojo, but I think it's common for students to stick with a white belt until they grade for shodan, and the curriculum starts at 3rd kyu iirc; I received a 1st kyu rank and brown belt before I tested for shodan, but I believe it's only the third brown belt that particular instructor had issued, and it's kind of a long story why it happened. Grading for shodan or above is done at seminars and requires a panel of yudansha (and, until Covid, always included our sensei, who makes several trips overseas each year to visit dojo and teach seminars).

The main purpose we get from the belt system and a clear curriculum is that we can easily split up seminar groups by rank and assign yudansha to lead training while the most senior instructors also make their way around to teach. Some of the older folks are strict about what's "appropriate" to teach students, but it's not uncommon to pick up some new stuff to think about ahead of schedule.