If the company use is basically websites + normal office stuff, then every platform has a web browser and openoffice or libreoffice. Not a problem. Big problem -- if the company says BYOD, but really means "you will pay for the configuration we want, instead of us buying it for you", then that doesn't work for me at all. My own device will run the OS and software I want, not whatever corporate wants. If they wish to supply a VM I'm fine with that, but my device means MY device.
A few additional problems:
-- What about viruses and security? Some of these devices that run Windows WILL get viruses and spyware eventually (home users do not follow proper security practices, and all to often do not run a proper virus scanner. As it is their own device, they may engage in high risk behaviors, i.e. bittorrent, porn sites, etc., that are highly likely to get a Windows computer infected.) Don't forget, at that point, they do not own that computer, the Russian or Chinese owners of the spyware effectively own it... and they can and will get all corporate information the user of the computer accesses.
-- If the machine breaks, who is responsible? You may think it's vital to get a broken computer up and running immediately, whereas the owner (who, after all, owns the device in a BYOD scenario) may not. Recall, if you expect the IT department to handle this... the IT department now, instead of being expected to support say a fleet of Dell model xyz computers (where they can even keep a spare or two on site), will not be as efficient being expected to work on whatever random model of kit the user has.
-- What about silliness? What if someone mainly types up documents and prints them, but decides that shiny new Ipad is just as good for it as their previous computer... but they can't type worth a damn on that little touchscreen, and can't print. It sounds dumb, but I've seen people glacially plodding at these before (tablets in general) while CONVINCED they are just racing through those screens. Or they get some $75 tablet that just isn't powerful enough, or bring their shit old Win98 system (believe it or not a few still are in the wild...)
Don't get me wrong, this is no guaranteed fail. But, I think in most cases it will be.