Briefly, near the beginning. But not for the rest of the video.
If you're watching a video on a phone, it's trivial to rotate the phone 90 degrees. On a TV or computer, not so much, so you end up with a ridiculous amount of wasted screen real estate and objectively inferior image resolution.
I found a discussion on the topic here[*]. The consensus seems to be that “wasted” sensor area outside the circle would not be marketable.
https://photo.stackexchange.com/questions/109452/is-there-an...
Suppose you implement horizontal recording while the phone is vertical; this would mean the video preview is now scaled and takes only a fraction of the screen (the same way watching horizontal video on YouTube while in "portrait mode"), which people would find annoying.
Alternatively, you could not scale the video; now the video preview displays only a vertical slice of the frame. It looks OK, but people would soon discover the actual video a screen's worth of image on each side of the preview, leading to anxiety and worry - people would have pay extra attention to not capture things that weren't intended to be on the video; they'd soon look for a way to turn this off.
The unfortunate reality is, it's a social problem partially caused by a technological one. Vertical videos are driven by the phone form-factor and because portraits and selfies actually need to be vertical, and people being people, shooting photos of themselves and other is what they care about the most.
There's far better things to focus false internet collective outrage at.
Contrast with a monitor, where it will at least be viewable vertically, even if it too only fills a portion of the monitor horizontally.