And if the company is worried about possible PII disclosure then strip names, contact information, etc... out of the resume and hand your people a stack of stripped resumes to browse through and select candidates.

Personally, I think there are a large number of people like myself that are qualified to do the job but are not good at "effective" resume writing and/or don't have well developed interview skills. I spent three years in and out of short contracts (mostly out) after my last full time employer laid me off during a reduction in workforce (most junior/least irreplaceable, my fault I know) and it wasn't until I was submitted to a company where my potential manager was the one who went through the applications and interviewed the candidates that I "made it through" the hiring process.

Hiring seems to me to be one of those areas where information technology still has a ways to go before it is a better alternative to having knowledgeable people reviewing each resume. Heck, IMHO HR isn't qualified to judge the qualifications of IT applicants in most companies.