I don't think it's a hack necessarily - as a well implemented time system would produce the same results at game rate = 0 as with pause.

Also there's a need for different time domains - like imagine, in a paused state the menu animations still need to play, or if the player enters a conversation, the game logic needs to pasue (depending on designer intent etc.)

Unity does this. You get scaledDeltaTime (when you set game speed to 0, it'll return 0) and unscaledDeltaTime (returns time between frames ignoring game speed). Pauseable logic uses the former. Pause menus use the latter.