What exactly do fighter jets and its pilots do during their peace time sorties?
As with any job, there will be some initial training to learn the basic skills needed, and that is typically done at a central location. But there will also be ongoing practice to maintain those skills and continue to improve them. Modern fighter jets are complicated machines and take a lot of knowledge and practice to operate. Simulators and classroom learning help but can't completely substitute flying and maintaining real aircraft. In the US, military aviators get about 20 hours per month of flying time. There's a saying in sports that "you play how you practice." When these pilots go into battle, lives are on the line, and they want to be able to recall skills they practiced recently, not years ago in basic training.