The Doctor defends Earth so much because he has to.
Just about every human companion the Doctor has ever had has saved his life at least once. Therefore, he has to maintain the history of Earth to ensure these companions are still born at the right time and end up in the right place to meet him. Otherwise, he’ll disappear in a puff of logic. And the more he defends Earth’s history, the more times his life gets saved by humans, so the more he has to defend Earth’s history. As part of this strategy, he keeps a copy of the Complete Works of Shakespeare in the TARDIS, and consults it frequently. If “Troilus and Cressida” goes missing, that means the timeline is broken at some point before Vicki is due to be born, and he has to go and fix it. If the entire book disappears, Shakespeare needs rescuing.