Why are examinees often not allowed to leave during the start and end of an exam?
Well the 10 minutes at the beginning is to allow some to arrive late without the possibility of collusion.

Where I work, it is 15 minutes at the beginning just for any who are late...

The 10 minutes at the end is probably to allow those rushing to finish a quieter time to concentrate - most students leaving manage to make noise - chairs scraping etc