Maybe, but people want to write applications that can easily interact with each other in a secure way. Trying to do that when your browser implicitly authorizes you no matter what the origin of a request is makes that extraordinarily difficult to do safely. Adding in the backwards compatibility problem makes it even worse because any solution is going to have to work with the existing methods.
What's the alternative? The webserver requests the third party resources on your behalf and repackages them into its own response?
You should be able to make REST requests anywhere, without caring about origin.