I'm talking about monitors with same width, like a widescreen monitor with 20" from the bottom-left to bottom-right against a square monitor with also 20" from bottom-left to bottom-right. Both will take the same space on your desk but the square monitor will offer more pixels and area. In such situation, all content and windows from the widescreen can be perfectly displayed on the square screen (with room to spare), but the opposite isn't true.
You say that different aspect ratios don't alter the experience meaningfully, but then you say that your 16:9 tablet is bad for reading books. So a 4:3 monitor in portrait mode will also be better for text related stuff (reading, browsing, programming, etc) than a 16:9 monitor. But even in case of video a square monitor is better since there's still a lot of 4:3 content out there, and a square monitor can play unscaled 16:9 videos and still have space at the bottom for subtitles that don't overlap the picture, for example.