I've seen how baggage handling is operated at a moderately sized airport - for flights that are currently being checked in, a baggage carousel is assigned per flight (in the back of house area). It looks a lot like the carousel you see when picking up luggage but instead there are luggage vans / containers parked alongside. The system sorts the bags onto the designated carousel and then a staff member takes each bag off the carousel and loads into the vans for the specific flight. If a carousel hasn't been assigned yet for a particular flight, there would be nowhere for it to go. In the airport I was visiting, these bags were sorted into a special "exception area" and they had luggage vans set up to hold them temporarily, sorted by hour based on the future flight time. At that future time, they would be re-inserted into the sorting conveyors, since the flights for that hour would now have carousels assigned, and only then would the bag make it to the van/container to be taken to the aircraft.
From this system it's evident that bags accepted too early have to go somewhere - in this case to a manual hold area. I know that larger and more automated airports have automated storage systems where each individual bag goes to a shelf for later retrieval. This is obviously expensive to install and operate and would still have capacity limits.
I think it makes total sense that low cost airlines would sign contracts with airports that guarantee bags would not be delivered to the sorting system too early, and therefore require extra handling and storage. Full service airlines would be more willing to pay the fees involved. It's all about you get what you pay for.