You can use it to identify unsophisticated attacks, sure.

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.