There are several reasons as to why a general manager must establish who their core is. For starters, the core are the players who should be the most responsible for bringing the team success down the line.
The Washington Capitals finally managed to win the Stanley Cup in 2018 and did it off the backs of their core in Alexander Ovechkin, Niklas Backstrom, Evgeny Kuznetsov, John Carlson, and Brayden Holtby. The same thing goes for the Pittsburgh Penguins who won in 2016 and 2017 with Sidney Crosby and Evgeni Malkin at the helm.