I hate the workaholic trope.
I think it's in the nature of a lot of head chefs to be workaholics. As Anthony Bourdain is attributed for saying,
"Few people have been in the restaurant industry as long as I have and are fit for anything else. Most of us who have been in it for a while are damaged in some way or another."
There's a reason why the Gordon Ramsay screaming asshole chef trope is a thing: head chefs, by their very nature, tend to be control freaks who want things done in very specific ways, and while a good restaurant is typically properly staffed, Gen doesn't seem to be. There's Shotaro, the head chef, and Arielle the prep cook/kitchen helper—she hasn't been shown cooking anything at Gen (I just went back to check the chapters since her introduction and she's only shown cutting and peeling vegetables at Gen, which is very basic prep work and not really enough to take that much pressure off the chefs), unlike Hans at Nobu, who has is definitely being trained as a full on chef, hence being allowed to develop his own dishes—working full time, and then Sohei drops in from time to time, but for a busy restaurant like Gen, that's probably really not enough bodies given the wide variety of dishes served there. Cooks and chefs have to work like they've got 10 more things to do because they typically do; the prepping and cooking is non-stop, and anything the cooks don't get done fall on the head chef, who typically ends up working more than any of the back-of-house staff unless they're a celebrity chef who leaves running the kitchen to the sous chef—in which case the work falls to the sous chef—because the buck stops with them. This is especially true for a diligent, non-confrontational head chef like Shotaro, who seems to be the type to take on more work than to foist it off on to others. Given how busy they seem to be, Gen needs Sohei to work full-time, and then they still need to get an actual line cook to even out the workload of making everything from scratch, but I think the nature of it being an isekai restaurant makes that task difficult.
Here's a personal anecdote about the nature of how overworked head chefs can be: one of the head chefs I worked under had a cardiac episode in the middle of a dinner rush because he worked too much, drank too much and didn't eat or sleep enough, which is pretty typical of head chefs (the bad life habits, not the cardiac episode). He was back working the very next day, because the restaurant couldn't really afford for him to take a day off. Restaurant work is nonstop, even at restaurants that close at least day a week—even those restaurants have to do prep and inventory and other things during the days when they don't have service—and Gen seems to be a restaurant that's open 7 days a week. In fact, that's probably why Sohei had shuttered Gen in the first place, because he himself was overworked; it may even have contributed to his distant relationship with his wife—who he clearly loves and clearly loves him back—because working at a restaurant can be pretty all-consuming, especially when you're in a position of responsibility.