Nice idea but does not work on my fully up-to-date iPhone 5s. After putting in the code and tapping "Pair" the pair button just flickers slightly and nothing else happens. Tried with two different codes, rescanning the QR code each time.
Assuming it would work cross device out of the box, because it _should_, was a idea I was comfortable with. I'll make it work.
Update: Works when I use Chrome beta on my phone.