There are tons of ways to approach your question. It's complicated, but by looking at historical examples, we can provide a general answer to why people tend to have others fight their battles for them.

Sometimes people are incapable of fighting their own battles and they need help. Let's look at World War II. Neither England nor France were prepared for Nazi Germany's fast and quick war machine, so they needed the United States to help them.

"We must be the great arsenal of democracy," said Franklin D. Roosevelt, the American president for most of World War II. Indeed, one primary reason why people have others fight their battles for them is that they have much in common already, like a belief in democracy, so their battle benefits other people—people who might be better equipped to champion their cause.

Another reason why people have others fight their battles for them is because their battles may be immoral, and they'd prefer not to be explicitly connected with them. Think about Saudi Arabia. It's been widely reported that Saudi Arabia gives money to terror groups, yet their alliance with the US and other countries compels them to try to conceal the evidence that they do this.

So why does Saudi Arabia fund terror groups when it’s supposed to be on the side of the US? Or why has the US supported dictatorial governments in Latin America and across the globe when it’s supposed to be a defender of democracy? A succinct answer is elusive, but a good place to start is by understanding that history is composed of people, and people have always had others fight their battles for them in order to either emphasize or conceal their interests and goals.