It isn't quite that bad, because the tests aren't independent. You end up with a few people who are disproportionately likely to test positive and can adjust appropriately your testing strategy for them.

And even if that wasn't the case-- you keep a few people home (them + close contacts) until followup molecular testing returns a negative. Yes, it's a big hassle-- you're "falsely" forcing 10% of the student body into remote learning, but probably better than remaining closed.