Well, not just cakes are stored in these; sometimes rolls, cookies, or rotisserie chickens. Also the joke is that we care it's loud because then we have announced that we are eating late at night. Sometimes this wakes people, and sometimes you just want to snack and not have a conversation, or at the very least be polite to people sleeping. Same with the microwave beeping three times loudly when you heated something up.
Also, "big cakes in the fridge?" implies that cakes are sold and stored by the slice. They are, but they also come in wedged shaped boxes made from this plastic. Also it is usually leftovers, like there was a whole cake, but now it's a third of a cake left on some weird slippery cardboard tray. You had a party, most of the cake was eaten by others, but you didn't want to waste the last bit. It takes up a lot of room, is fragile, and spoils quickly. But your significant other is on the couch sleeping off a hangover, so being quiet is considerate.
I watched a instagram video recently where the guy was up at 2am and decided it was a good time make brownies. I'm like dude these days at that time it's usually a my first restroom break as I've been asleep since 10pm. It's not time to whip up gramma's brownie recipe from scratch...
I remain convinced this device was originally designed specifically to make as much noise as possible, and was only later used for storing baked goods.