Overprotective boyfriends and girlfriends are a popular character type in romance, and bodyguards are the zenith point of that trope. Bodyguards are assigned to guard a person who is powerful and precious, or someone who is related to a person in power. They need to be careful because they have a target on their back, and characters like Hagi from Blood+ and Yona Of The Dawn's Hak take their jobs seriously.
Source:https://www.cbr.com/anime-bodyguard-romances/