Most of the teachers in my son’s school do pretty much what the OP describes, let the kids see the tests in class, but then collect them and don’t let the kids keep them. (I have no idea what a test center is.)
Frankly, I chalk it up to laziness, pure and simple. This generation didn’t invent cheating. When I was in high school, teachers gave us back our tests. They could be useful for studying for the final. In college and law school, many professors would put previous years’ tests and exams with sample answers on reserve as a study aide before exams. But my son’s teachers can’t be bothered to write a new test each year. In case you’re wondering, I jump to the explanation that is highly critical of the teachers because this is just one one of many examples of laziness from the teachers in my son’s school. #notallteachers