"Surely schools are more than capable of implementing such a policy for themselves if they believe it is best for the kids."
It's easier for the school to be able to just say it's out of their hands. The objectives are also national: Better education, less well-being issues, etc.
Most early education needs to be soaked up rather than looked up. Later, there is value to looking things up, but not during an exam or recalling something that was part of the last night's homework. With more and more voice input tools, reading and writing can suffer if not practiced and if the information returned is incorrect or not appropriate to the questions being asked, how would one know? One of the main tactics of multiple-guess quizzes is to quickly eliminate the couple of "not even wrong" outliers and consider the remaining choices. If you've done the revision, the correct answer should stand out or at least trigger a gut feeling. If you just press the easy button after school/uni, that's up to you but the imposed drudge work will have forced at least something through the thick skull up to that point and maybe that's enough to keep a marginally more clever person from tricking you out of your money.
I really should take up working somewhere at the till and seeing how much I can make each week by short changing people. With so many people thinking arithmetic is hard, I'd be in a new car in little time.
The little faces of the fast food workers really glaze over when I seem to hand them too much money and force them to punch the numbers into the register. It amazes them I can do "the math" in my head to get back a tenner instead of a wodge of change.