One thing doesn't have anything to do with the other. Kizaru was on a time limit. He had to get to the crew before they can escape and he failed because of Ray which made him back off. Hancock was right there but BB didn't even attempt to fight Ray.
Okay lets get the facts straight since admiral fans still cling to shitty "Oh he huffed" panel
-Upon meeting Rayleigh Kizaru already started complaining "I don't have what it takes to capture you right now"
-Then his complaining evolve to please don't make me look bad
-Then he is frustrated, like literally frustrated Rayleigh has him by the balls and he can't stop Kuma from ruining his plans because of it
-Then when its all said and done when Rayleigh is done ruining Kizarus plan..Kizaru still doesn't have balls to fight Rayleigh..knock him out and capture him. Rayleigh is standing there with zero fear and this is man with one of the highest Bounty ever and 2nd biggest criminal ever and man who knows about void century
-Then he takes out his frustration from Rayleigh on Fodder Pirates
-Then Sentomaru tells us 2 years, literally two years later Uncle Kizarus ass was fully stopped in his tracks.
So maybe instead of applying mental gymnastics and point fingers at each other just acknowledge RAYLEIGH IS THAT FUCKING GUY
old Rayleigh is Yonko admiral level
Prime Rayleigh is pirate king level
Simple as that.
Don't over complicate it just accept it and move on