I know recruitment firms serve some of the phone screen purpose you’re proposing, but just with basic Q/A of resumes.
I think, if I were looking to hire you, I’d be wondering how alike your working style was to that of me and my team. I’d want to know how much I could trust your judgment in a candidate’s technical approach.
I’d also offer that you can’t really outsource the job of evaluating cultural fit - which is still really important in spite of all the baggage that term carries.