In my experience, about 80% of the candidates who send in their resume will not come close to working out. If you've never run a hiring process before, you'd be surprised how many people look decent on paper but somehow can't write a line of code without some serious hand-holding. The OP points out that sometimes the opposite is true (a candidate with a mediocre resume ends up being stellar), but this is an exception and you'll waste a lot of time trying to find these people.
I've honed my resume screening skills over time and I've gotten pretty good at filtering out most of that 80%, and I know I'm likely to screen out plenty of talented folks, but it's well worth being able to focus my time and my team's time interviewing more exceptional engineers than mediocre ones.
In other words, I think it's OK to throw out a lot of the baby with the bathwater as long as you're left with mostly baby.