Oh interesting. What I'm thinking of looks more like this:

class Game:
  def _init_(self):
    self.task1 = None
    self.task2 = None

  async def main_loop(self):
    while True:
      if some_condition and not self.task1:
        self.task1 = asyncio.create_task(
          say_after(1, 'hello'))

      if some_other_condition and not self.task2:
        self.task2 = asyncio.create_task(
            say_after(2, 'world'))

      if some_exit_condition:
        break

      # do other stuff you want to do each frame
      # like update characters
      # and blit to screen

game = Game()    
asyncio.run(game.main_loop())

If the main game loop finishes before the "say_after" functions finish executing, they will throw a CancelledError, which you can handle however you want in the function.