There is no rule like that. I'm an Indian student. All exams have different rules. They sometimes ask you to keep phones outside, sometimes near the invigilator, and maybe even in your pockets. Some also refuse to let you use the bathroom throughout the exam (usually 3 hours)
But students always find a way to cheat. Nothing will stop cheating.
Even what you described, is ultimately aimed at preventing the student from accessing heir phone during the exam.
Even my sources are the same. I took multiple national level exams organized by the government and private colleges just a few months ago.
The phones arent even allowed inside the exam hall. You have to keep them outside for national level exams.
Even pen / pencil boxes or pouches are not allowed.
Bathroom trips are usually not encouraged.
In India, all students are supposed to turn off their phones and keep them on the teachers table for the whole duration of the test. Having a phone on person is deemed to be cheating and failed in the test.