I run two 1080p monitors in portrait on my desk at work. It's unreal how many interfaces assume you're widescreen: images are cut off abruptly after they scale to the width of the screen, horizontal scrollbars appear as default widths of panels in apps assume a widescreen monitor, and Excel spreadsheets flow off to the right. I'd love a 1920x1920 monitor.
1080 is absolutely not wide enough for today's software and web sites, but 1200 is mostly manageable. Anything that is too wide for 1200 either has too many columns as an attempt to use the absurd width of most monitors, or its lines of text are too long to be readable.
Another issue I had with a portrait monitor is, once you hit a certain size, you don't use the extra vertical real estate. You wind up moving your head up and down (mostly down) and you leave your head like that for a while sometimes. It's terrible for your back and neck, even standing.
