I worked at Hardee’s in the early 1990s, so things have probably changed drastically there in the back room, but at the time, we had the main reasons that we didn’t do it was the lack of space on the grill and prep table.
We also had the opposite problem, people wanting lunch items at breakfast.
Some items we could have made easily all day (and if a customer asked, we’d make it): pancakes (which were simply tempered from frozen and kept in the cooler, then chucked in a microwave), biscuits, bacon, and the little country-fried chicken steaks that we sold at the time.
Problematic would be eggs, sausage, sausage gravy, Canadian bacon, country ham, hash browns, omelets with special fillings. The gravy required a bunch of sausage patties to be grilled and chopped up, a pot of water to be boiled, and the gravy made… a process which took about 10 minutes, monopolized valuable grill space, and took an employee away from the prep station–someone who couldn’t be spared from the prep area in the middle of a lunch rush. And gravy got gluey really quickly; the morning batch was okay for a couple of hours, but we couldn’t keep making batches and throwing them out through the day because of the chance that we might get one order an hour for it. Everything else took up valuable grill space-- the process we used would have required us to use 1/3 of the grill for a single breakfast order, grill space we were loathe to give up when we were selling so many lunch items that the grill would be completely full of hamburgers at all times from around 11 AM to 2 PM; a breakfast order would have take about five minutes to make for the customer, and would put us five minutes behind on all lunch customers… and that time can add up quickly, since people don’t want to idle in drive-through for minutes on end.
I get the feeling that customers never understood just how busy we were in the back during lunch rush and dinner rush (5 PM to 8 PM or so). Six people working as fast as they can to keep up; the bun toaster and the entire surface of the grill were in constant use churning out hamburgers, two people were assembling sandwiches non-stop, and there was simply no time to do anything else. I think this is the other reason that so many fast food places don’t do breakfast all day; the backroom turns into a fast-moving assembly line making one primary thing: hamburgers. We literally had no time to stop. The backrooms are actually engineered to minimize walking by employees, so they were purposefully kept small, and there was no way to fit a second grill back there. Breakfast rush was slower, so we could spare the majority of the employees to do all the stuff like preparing biscuit dough, chopping/slicing vegetables, etc., while one grill guy and one prep station guy could handle everything. At lunch and dinner, it’s all hands on deck, and there’s no more time for prep.
Hash browns wouldn’t have been so bad if the customer could wait 3 minutes for them to fry, and we did do it for customers who would wait, though it absolutely killed our order fulfillment times. Sonic gets around this by simply doing only tater tots, no fries, so they can cook up a batch and keep them under a heat lamp with the reasonable suspicion that they will sell most of them.