I think what the OP is arguing is that if he has an active github profile: 1. the recruiter should have done the work to check that out before emailing him. 2. his/her profile should be enough to warrant arranging a meeting/interview, and a resume would add little extra information.

If you don't have an active public place where your work is showcased, then certainly a resume is a good (more) private way to provide a potential employer your skillset. Though certainly not the only other way.