Or how some armies burned bridges behind them.

I believe in this case armies were showing that they were fully committed to your enemies. It was a demoralizing act to defenders.

The same might be said of startups. Quitting can signal to others (investors/potential employees/customers) that you are serious. However, I feel like this thread has taken an introspective slant. I'd caution anyone quitting who is trying to signal to themselves.