The simple explanation makes sense, but I'm realizing there's a subtle point here that I should been more clear on.
They might not be filtering out the bad at the expense of the good. But filtering out some of the good in the name of saving the money it would cost to develop / administer more general assessments.
That's the p(interview_capable) piece whereas the trade-off you mention is the conditional probability (also important!).
I don't know about US, but where I live they hire you with 1-3 months "trial period" during which the company can fire you any time if you turned out unfit for the job. This is exactly your proposal.
Because the cost of hiring the wrong person is a LOT higher than missing out on the right one.