And that is an assumption based on Carmel merely mentioning the CD in the same sentence as the Admirals ?
Cipher pol is literally the only force the Government has at their disposal next to the Admirals. It's only logical to assume that Carmel expects an abnormal strong warrior that isn't an Admiral in to become a CP0 member, it does not put them in relation in terms of power.
The only thing that Carmel directly confirmed in that sentence is that Fleet Admiral > Admiral.
It's not a mere mention, she knows what she's talking about. Oda wouldn't have made her say it if he didn't want to make the readers see it that way.
Let's wait to see if the fight went down the exact same. Lucci got up and could've retaliated but chose not to because he was outmatched. A world of difference from being knocked out and not getting up at all.
You don't have to stay knocked down for days to declare you've lost a fight. For all we know, it could be an attack weaker than Dressrossa Luffy's G4. That won't prove anything in the grand scheme of things. We're blowing this out of proportion for no apparent reason.
Accept that Admirals are endgame material antagonists held back via plot because the crew is not ready to face them at this current point in time. Oda works his way up the ladder in terms of Government forces. First he lets Luffy beat the CP0 and after that the Admirals.
The admirals aren't end-game materials, they're just major antagonists just like the Yonko. Everyone already knows this. If they don't know it already then they're not paying attention. There is no need to drag down the Yonko to prove the admirals are great. If you do that, you aren't any more logical than the Yonko fanatics at this point.
As for Lucci vs Kaido. Lucci does have Awakening confirmed, Kaido didn't. Whether drunken mode was his awakening or not is only our assumption which never really was confirmed. And then we can open up the discussion of the Beast pirates treatment in terms of giving the calamities Awakening etc.
Doffy, Katakuri, and Kid have awakened their DFs. All of them are stronger than Lucci. Pit them and Lucci against Kaido, he'd wash them. So it doesn't matter if he has awakening or not.