I've been doing this awhile, and I've seen hiring work really well without the LeetCode grilling.
And I've almost always seen the LeetCode grilling be administered by someone who doesn't know what they're doing (and often also tainted with ego, despite the strange claim of some that a LeetCode grilling is objective).
That said, if you're sourcing random people, good luck, it's a flood of LeetCode gamers to wade through, and too much of your staff interviewing them might also be LeetCode gamers with no experience doing non-LeetCode interviews.
> Edit: BTW, where did you see Google saying their interview process doesn’t work?
I have a bunch of notes on Google hiring I'd have to dig through, but the first link quick at hand is this retrospective by a hiring committee person who left (and I have a note about 8m50s being a funny story of the hiring committee realizing that they would've rejected their own packets): https://www.youtube.com/watch?v=r8RxkpUvxK0 (IIRC, I don't agree with all the beliefs he still holds, but he calls out a lot of problems they found.)