He is probably doing this to keep the health inspector happy. But I agree, 7 days for some things is not going to work. Hopefully, he also allows the cooks to make judgement calls regarding this. There is no way that cut melon is going to be good after 2-3 days, let alone 7. Sure, it might be safe, but it is going to look and taste like crap. Most leftovers, but not all, would be pretty scary after 7 days.
I was working for a company that took the opposite approach and many of the things that we labeled needed to have use by dates well before things had a chance to turn. In larger units this wasn't a problem but in smaller units it created lots of unwarranted waste and higher food costs than they should be running. Open a 5 pound bag of cheese and you had 7 days to use it or it had to be thrown out. Slice ham, turkey, roast beef, etc. and no matter how you stored it, apart from freezing it, you had 72 hours before it had to be tossed.