Just code up a 5-line simulation and see what happens? You do actually expect the server to eventually recover from all load spikes, but that dead time means c

Just code up a 5-line simulation and see what happens? You do actually expect the server to eventually recover from all load spikes, but that dead time means cumulatively you'll typically have queued more requests than you've handled at long enough time scales. On average that surplus is infinite, despite it sometimes being as low as 0. It's not just academic, but it's not surprising that doesn't echo your real-world experience either. We don't usually run systems anywhere near capacity, and even when you do you'll still expect the queue to be able to handle the load eventually.