I'm a manager of a small staff and if one of my employees has an emergency (family issue, personal, I honestly don't care) I consider it my job to fill in for them for the rest of the day.
Yes, I have my own shit to do, but I shouldn't have so much that I can't prioritize and help out. Would be poor time management otherwise. But what about your whole staff constantly calling out? Did you look at an honor their availability? If for some miraculous reason you answered yes then you are understaffed. Hire more people. Plain and simple.
Can't hire more people? Increase the pay to a living wage and fight the best you can to get the company to realize you need make a slight cut to the profit margin. My master's was on profit margin in the restaurant industry. There isn't a single industry in the US that will collapse with a decreased profit margin. Now for some reason you did increase pay and no one will work any more. Do you treat them like a human? Listen to their needs? Desires?
Now managers are you overworked? and no matter how well you prioritize or schedule you have too much to do? Sounds like upper management is playing you and they need to hire more people? Maybe that AGM position has been vacant for 3 years because that was the only way you could actually get a pay raise. Well you are burning yourself out even though you do deserve that raise.
I hope management can see the cycles they are making for themselves. I am far from a perfect manager, but fighting for correct staffing has allowed me to increase retention rates by 50%. That may not be a big deal, but to an employee it can be. (Wether it should be is a whole other discussion)
TLDR; Management is in a spiraling cycle that they created and could easily get out of by recognizing the obvious signs. Treat employees like humans, actually fight for them instead of saying you are going to, a d recognize when you are being abused yourself.