Well, our parents, and for the younger, our grandparents too, and us, have managed to do fine for like 60+ years of using fridges without an fridge door alarm.
Fun fact: for an alarm for when you are away for days, and you want to know if the fridge power went off and back on in between, you can freeze a jar of water in your freezer, put a coin on top, and leave it there.
If you find the coin in the bottom of the jar at some point, the fridge power/temperature has been off for a while.