I'm not a fan of Sketch's Insert menu. It's hard to see the tiny symbols in the list and on top of that if the symbol is meant to use overrides they are ignored when placed via the Insert menu.
There's another way to set up your design system.
1. Create two files. One for your team's Symbol Library and another for the Design System
2. In your Design System file link to all the symbols in the Symbol Library
3. All designers download the Design System folder and link the library in Sketch
The designers on your team can either copy and paste symbols from the Design System to their own files or use the Insert menu
All symbols will get updated when the library is updated. Also all overrides comes with the copied and pasted symbols. This setup scales well across 6 or 60 designers.