A big reason for this is that it breaks a fundamental contract of web interaction, in place since the beginnings of the web, that users have come to rely upon.
How have users come to rely on GET? Ok, it makes a useful "Would you like to resubmit this action?" popup when you click the back button. And it can be useful to prevent XSF attacks. But neither of these is really relevant to frictionless sharing. Really the only thing I can think of that may be problematic is the possibility that spammers might be able to use it for spam. But then again, I'm pretty sure I violate HTTP on a daily basis. Maybe I'm one of the bad guys.
How have users come to rely on GET? Ok, it makes a useful "Would you like to resubmit this action?" popup when you click the back button. And it can be useful to prevent XSF attacks. But neither of these is really relevant to frictionless sharing. Really the only thing I can think of that may be problematic is the possibility that spammers might be able to use it for spam. But then again, I'm pretty sure I violate HTTP on a daily basis. Maybe I'm one of the bad guys.