Frankly, I think you either didn't do a rigorous experiment, were fooled by randomness, or (most likely) aren't hiring top talent.

Interview loops are an enormous investment of time these days. I'm not going to take one unless I'm confident the offer will come out in an acceptable range.

Maybe you can fool some people with less experience or market power by not giving them the comp info upfront. But not the best.

And don't be surprised when any truly talented folks among your hires leave much earlier than you hoped. Karma.