The tests don't just help you think about the code, they force you to do so. For those who are tempted to think "I can just do this quick change this one time; nothing will go wrong", tests force you to actually think.

Or they don't. If the tests just continue to work, then you ask yourself whether the change should have broken them. If not, you go on your way with a fair amount of confidence. But if the change should have broken the tests, then you have to look at why it didn't...