Excuse yourself to go to the restroom, use phone hidden there the day before. That's a viable method of cheating in many countries, I guess cutting internet access is a way to prevent this and similar exploits.
I suspect all of Wikipedia's text fits comfortably on a typical user's phone. How does not having Internet access during the exam stop people from accessing data they've already gathered from when they did?
In certain parts of the world you can bribe the invigilators.
How does this relate to internet access?
You bribe them to not notice the phone you are using to help you answer exam questions. Without internet access that's more difficult.
it's about minimising damage in the case of questions leak. The exam paper is the same across the country, so if a paper is leaked from one school, the internet would quickly make the problem nation wide.