The school arc has time skips in the LN. The development of the MC's interpersonal relationships is an important part of the story. The MC will also be staying in school until his 20s, so skipping all of it will be problematic for the story telling process
Schools are great places to introduce new characters that could be important later on. It's a natural gathering place for people who are near the MC's age.
A novel that I read actually gives a plausible reason for reincarnated people acting differently if placed in a younger body. A younger body's brain is less developed so it could affect the thought processes of someone reincarnated.
Knowing what would happen in the future doesn't guarantee that things will happen exactly the same. Since you have the knowledge, it could affect how you react to events that lead to the previous future which would then change the future in this current timeline.