So here's the thing... hiring at larger, growing companies often means weeding through a stack of a hundred resumes, for one or two or five roles. Most of those resumes need to go away. The interview process, for competent candidates, is going to cost you at bare minimum a half hour of one person's time for initial screening. A quality interview is going to take a couple of hours each for a few important people - man…
"Let me randomly filter these and hope for the best" is the essence of your suggestion for screening candidates. It doesn't sound very good. It sounds like you should be investing more time into interviewing more people instead of throwing away folks who could excel, but fail an arbitrary heuristic. That is to say, instead of throwing away 19 out of 20... don't throw away so many. Obviously you don't need to call in…
If I have 100 resumes for two roles, and I can, through heuristics, knock it down to five, then I'm starting with enough "good" resumes to stand at least a chance of filling the two roles. Mind you, we're now about a day's worth of work for a manager, and five interrupted afternoons for the senior/lead engineers doing the interviews.
On top of that, the good candidates are going to have other companies competing for them. If my response is "Well, we like this candidate, but let's spend two weeks interviewing another twenty people, just to be sure", my odds of missing the good candidate are pretty high.