I apply my skill points from last season on day 1 and won't apply skill points again until the start of day 1 the next season. Some advantages:
better cup draw
easier to identify fast/slow trainers
cheaper to renew contracts at the start of the new season
can learn new role or skill instantly
easier to identify players I want to (or don't want to) power train at the end of the season
Every player's value goes down as they get older. If you apply skill points everyday, their value will go up slightly each day. When the new season begins, the value drops. Then it goes up again. But if it is a young player (a lot of skill points), the value dropped is less than the value the player increased over the course of the season.