I just dropped my old Samsung Galaxy Tab E9.6 and the screen is badly cracked with bits of loose glass, but the LCD still...

Have you checked for dust? Dust buildup outside the fans can also block airflow. I just replaced my fans because they were constantly spinning at top speed and not cooling, and while the fans themselves were dusty, I found far more dust in a thick layer just behind the fans. It's also possible there's something else blocking the airflow. The less obstruction to the airflow, the more efficient the cooling, and the less your fans have to spin.