In addition to not having the time to think, we also usually suck at thinking.
Our society fails badly at teaching people how to use their brain properly and how to prevent it from going on a bender.
The best advice I've heard on this subject so far is to think when there is a specific problem to be solved. Use your brain like a tool, then stop using it after you're done - meditate.
Very hard, since thinking (and overthinking) is addictive.