The Origin header is not as good to prevent CSRF since it's a known value. A CSRF token is a one-time value generated in the server, it's impossible to guess or get a valid one from the outside.
Nonces have the benefit of only relying on browsers preventing cross-domain reads.
When Flash is deprecated, and if a site wants to use CSP, then this might start looking like a better trade off.
ATM though, nonces can be automatically added to all same domain forms on your site with JavaScript and you can check it trivially on all POST requests, getting most of the non-CSP related benefits without waiting on browsers.
And even if browsers were to implement it, there is still a long tail of browsers out there that will take forever to update.
However, if someone has the ability to make malicious HTTP requests on my behalf using my browser can you really be sure that they don't have the ability to make malicious HTTP requests with altered headers through a malicious extension or a browser specific exploit or some other vector?
You still have to do all the other attack mitigation strategies in addition to checking the Origin header, and I'm not sure the extra complexity buys you anything in the long-term.