I suggest this video as it also goes into detail for why you use hooks in the first place (Beware: he is a bit sloppy with foot/hip rotation, else very good video). If you look at it, there are some points to consider (everything for the left hook, like in the pictures):
The right side of your body isn't exactly "exposed" as it is turned away from the opponent.
Compared to a jab, your left side is equally vulnerable for an opponent who goes in with a body shot.
Most importantly: To have your right guard getting away from you and opening up is actually bad technique. Especially the guy from the first video you linked does unconsciously use that arm to gain more rotational momentum in the shoulders. His rotation and whipping are very good and powerful but opening the guard is a technical weakness of his, not tied to hooks as such.
In the video linked above, the teacher has better form and tells us to lift up the elbow, create a 90 degree angle between biceps and forearm, and then rotate the knee and hip to initiate the shoulder rotation. He also reminds us to keep the guard up and close:
The trick is to get used to the power generation of hooks so that you learn to get fast in, fast out. That way, it is not any more open than a cross punch. It does have a completely different application in a slightly different range though. With good footwork and slightly pulling a centered jab-cross-combination (so that they have a shorter range but still hit), you can get into range without your opponent noticing. Also, you will force their guard into their center. Then you finish the combination with a hook behind their guard. And this is only a very simple example to give you a rough idea of what is happening.
I other words: You have your guard up and close in hooks as well, and it is a tool that can and has to be used in unison with footwork and straight punches. With straight punches only, you will eventually end up hitting the guard only.