It's fine to ask kids to go when there's specific opportunities, but that doesn't justify restrictive policies during other times: Tiny bladders of small children don't work that way. Especially in grade school, it doesn't need to take more than 15-20 minutes to go from "I'm fine" to "I a really need to go". Especially when bathroom privileges are rationed out & tightly controlled and you become hyper aware of your bladder state. I have my two young kids "do a try" in the bathroom before we leave the house for any car ride. That doesn't stop the occasional "I have to go!" 20 minutes into the trip. And sure enough, at the rest stop it's like my kid turned from a 6 year old into an elephant from the amount that comes out of their body.
When & how quickly you develop the need to urinate depends on a lot of factors: Your specific metabolism, recent activity, what you drank and ate, body position, and probably more. And at some point mentally, you simply pass a threshold where one minute you feel no need to go to the bathroom, and the next minute you do. If that "next minute" occurs 10 minutes after lunch break, so what? What is gained by denying that need?
It was actually harder in high school because other than lunch, you had minimal passing time between classes (just a few minutes) so if you stopped to go to the bathroom there was a good chance you'd be late to your next class. And of course no recess. Lunch and P.E. were the two chances you had per day to use the bathroom without having to ask.