Because you want other apps on the second screen?
Is that so you can be distracted by them and work less efficiently?
LR's not exactly a drag and drop kind of programme. As you've correctly mentioned before, you manage your files from within LR and export things out form there. If you simply drag an image out of LR to a different folder, you lose any work. You can drag images to import, but if LR is using entire desktop simply drag to the LR icon in Dock and it's the same as if you drag LR itself. I use keyboard shortcuts in LR to do imports even easier.
Alt/Cmd + Tab takes to another app if you need to go there. I've always used my software to fill screen or screens and swap between them, less clutter and more efficient. Never understood why people like to waste waste time dragging windows around screen with mouse to access other programmes. Maybe they want RSI.
Sure, Lightroom's second screen is a bit awkward, but I agree with the comments about people using bigger screens. Plenty of other improvements would be more worthwhile.
Yet dual screen support was a very popular request when it was absent and now the same people would like it to have been implemented in a more useful manner. Being able to have library module on both would be very useful when file managing or as many people have said, having Library module and Dev on separate screens would be nice.
A bigger screen would make makes no real difference to how LR works either [for me that is, besides I have two of them.
] If anything unless you hack LR, I'd imagine the side panels get less easy to use the more pixels you have in screen, can't test theory because I already hack LR to get panels that are useably wide enough. Maybe if you use the film strip at bottom....I don't as I have a second screen and find library is much easier to use if I only have one screen, such as with laptop.