"Proper color management" on the web as I see it is that all graphics that has no ICC profile associated is displayed as sRGB, and all other graphics according to the provided ICC profile. This is how it works on the Mac.
On Windows and Linux it's more complicated. Using Firefox web browser and setting gfx.color_management.mode to 1 you get the desired behavior (and that is how I run it), unfortunately this is not default, the default is instead to only color manage the graphics which has ICC profile, all other is stretched to the maximum gamut. I think this is also how Chrome works currently, not sure about IE/Edge, but it can easily be checked.
The poor color management on key Windows applications is holding back the progress in using wide gamut screens unfortunately. On the Mac you can use a wide gamut screen and not knowing anything about color management, while on Windows you need to know at least something.
Windows as an operating system has good support for color management, but of course you need to calibrate your screen and install a profile for it for it to work. And then it will only work for the applications that choose to use color management and do it right. On OSX if an application does nothing it becomes sRGB automatically, which makes it easier for the we-don't-care-developers. The reason Windows is like it is I think is historical and something to do with the APIs, you're closer "to the metal" in Windows, it's good when you want to do high performance stuff like games and advanced graphics, but less good for less advanced applications as they don't get color management for free.
Until Windows is as easy as the Mac concerning color management and wide gamut screens is the new standard unlike the specialist tools they are today you should publish sRGB to the web. It's always good to embed an ICC profile too.