>Surely resumes are the only way to deal with the volume of job requests some companies get?

This is partly true. It is truly shocking to me how many resumes has spelling and grammatical errors. If there is one single document you will ever write that must be spelling and grammar error free, it is your resume. As soon as I come across a single spelling or grammar error in a resume, it immediately gets trashed. I don't care how good a programmer your are, details matter. If you are going to be sloppy with your resume, you are going to be sloppy with the company's code.