Kaido's been saying he'd kill Yamato for the past two decades, but he didn't! And he announced his plans to make heof r the nest Shogun literally in the middle of the fight; not that hard to see he's bluffing to get her to obey him. If Kaido really wanted to kill her, she wouldn't be alive until now, period.
She did have some impressive showings and matched Kaido's low-end moves but she was also consistently getting outdone by her father more times than not while Rayleigh did not even leave an opening for the fastest character in the series to get a hit on him. It's harder to not let a top-tier land a hit on you than it is to get consistently beaten and get back up to fight, because most non-top-tiers could do that as we've seen with Kid, Law, Marco, etc.
And it's not like Rayleigh was going all out against Kizaru or anything. He too wasn't using CoC coating and possibly even adv. CoA, yet he was matching Kizaru blow for blow while Yamato was going all out to not get killed by Kaido, who's obviously not going all out. That's why separates Rayleigh from the likes of Yamato or even Zoro for that matter. Again, saying Kizaru is much weaker than Kaido is a groundless claim.