Currently, the AGameState actor derived from AGameStateBase provides a lot of useful game framework events when using AGameMode such has handing when a match has started and ended. It would make a lot of sense if these hooks were exposed to Blueprint as if you’re using AGameMode in blueprint and want this functionality, you essentially have to build a second copy of all this logic to handle it. Alternatively, a more drastic and most likely unfeasible option would be to remove this functionality altogether and leave it solely up to developers to build this logic themselves.
Most of this related logic in AGameMode is already exposed to Blueprint and has relevant hooks for catching match state changes. It seems like not exposing this stuff in AGameState is just an oversight.