> The point of centering an element horizontally is to make sure that the content you’re viewing is directly in front of you.
That's an awfully big assumption. For starters, you're assuming that the browser window itself is centered on the screen, and that the device is centered in front of the user.
I don't think this is the point of centering an element horizontally at all, and the result you have created here is not at all what I as a user want.
I use Firefox with a vertical tabs extension open all the time. Occasionally (rarely, mind) I run into sites that don't bring their full content into view unless I hide the tabs list.
Guess they think like the OP.
I used Tree Style Tabs until recently, and never experienced this. Also now with the native vertical tabs I've never seen this.
It almost never happens. And when it does it may be some other broken calculation. But I did run into sites that I can only guess did their layout based on the whole window and had stuff go under the tree style tab.