My point is that it's very understandable that such possibility would be useful for some people, and that they would very much like that workflow. It's just that if they are a minority - the industry will not prioritize such development, and it's a good thing. This means that they will develop more needed features.
In a way, everything you describe already exists in the form of Web Apps. Log into Gmail on your PC, do some things there, then switch to an iPad and open the same address there. - voilà you have same app on multiple devices. It will even sync flawlessly...
Regarding file sharing - I can only speak for the technologies that I've been using personally, but both Samba, Dropbox, FTP, SFTP bluetooth filesharing and bluetooth sound have all been working amazingly great for me... It seems like a perfect example of a developed and implemented standard which most devices agree on. What am I doing wrong?