It sometimes does happen. It’s called a tail-strike where the rear end of an aircraft touches the runway. It can happen during take-off if the pilot pulls up too quickly. It can also happen during landing if the pilot raises the nose aggressively.
Why are the wheels arranged like that?
Almost all the modern passenger planes have a landing gear arrangement called tricycle undercarriage in which there are two or more main wheels under the wings and a third smaller wheel under the nose. This means almost half of the plane is protruding behind the main wheels.
An illustration has been made to show that even 10 to 20 degrees rotation can cause a tail-strike. If you have ever been on a see-saw, and the other person suddenly jumped out while you are up, you will suddenly fall and hit the ground. This is somewhat similar to that.