How much would better would your hire be considering that you managed to check all 1000 of them, rather than just 50?
Assume that candidate fitness is a number normally distributed around 0 (half of them obviously being negative), that both you and the AI can perfectly pick out the best candidate, and that you picked the 50 to interview completely at random. The average actually seems to be around 40% better? Suprisingly decent. Is that improvement worth 1000 man-hours?
So attempt two here: maybe instead of each company sending candidates through an interview, there should be a common gatekeeper. All working age people take the same 1-hour AI interview, and the glorious overseer assigns them to the position they are best suited for.
(An actual answer here is you assess how important it is to get "the best candidate", and you interview enough people to get a reasonable approximation. The hour cost on your side is what keeps you honest. If wasting candidate time is free on your side, you're going to waste 500 man-hours of work for a 5% better result for you.)