At my kids' school (I work there and help at the Cafeteria too):
Kindergarten has lunch at 10:45.
Lunch times for each grade level, is per the timing, as you said. And per the capacity of the cafeteria... and per the saneness, of the kids all being there at the same time etc.
At my kids' school, the timing, does not overlap. BUT, one grade level that is leaving lunchtime, MAY overlap with the incoming kids (ie: the next grade level).
Per Kindergarten, at my kids' school, the kids do eat and are hungry even at 10:45am. I SEE them eating and being hungry. **BUT.... if a kid has a home lunch, and it is something they do NOT like... the child will NOT eat... EVEN IF HUNGRY. I... see this ALL THE TIME. A kid simply will NOT eat... if the parent makes some home lunch that is not something they like. So, keep this in mind.
Now, per my kids' school, the kids ALL bring, water-bottles to school for drinking whenever (the Teacher allows that), AND they bring their own snacks (the Teachers allow this)... and Snacks, are eaten during recess times. Per Kindergarten, at my kids' school, they have recess after lunch, and one in the afternoon.
IF a kid is hungry, at any other time, if a kid tells the Teacher... the teacher, per her/his discretion, will let a child eat something. Because they are young.
The timing for lunch periods, per grade level, is timed according to the length of the school day overall. At my kids' school, which is thru 5th grade... it takes about 2.5 hours, for ALL the grade levels to have their lunch period.
And YES... MOST kids, are HUNGRY after school anyway. This is a given. They are very active in school. And they need a snack after school.
My kids, eat before going to school. My kids are 5 and 9. 1st grade and 5th grade. I TELL them, that they need to eat, because of their lunch times. AND they bring a snack to school to eat during recess. AND they bring water bottles.
Depending on my kids' appetites in the morning, they eat according to that. Then they go to school. AND if my kids "chose" not to eat much in the morning, despite my explaining to them... then they went to school, without much in their tummy. THEN, I let them... learn that way- ie: if they don't eat in the morning, they get HUNGRY and before lunch. So, once they learned that, they ate in the morning. Even if that was a yogurt.