If all you need is evidence then mobilizing an admiral is a bad idea, that significantly weakens the main force and leaves them open for threats like a yonko attack.
Here’s a bunch of non-admirals assessing the situation in Alabasta and then stripping Croc’s title away after a 1-minute call with HQ:
The hard part is actually having the muscles to beat Doffy and drag him to prison afterwards. Kuzan’s statement is also implied about strength, it was clearly worded that way to hype Doffy.
The purpose of the admirals is literally to be rolled out, he's not the fleet admiral who is to reside near Marine HQ. Hence Kuzan could bike around anywhere he wants without a care in the world.
I'm already aware of the Crocodile panel, but completely ignoring all of that happened after the strawhats had exposed him and the rainmaking powder which is banned. Along with a giant conspiracy against one of the founding WG families. Thus the WG revoked his license. That would be the equivelant of taking away Doffy's title after Luffy whoops his ass and exposes the underworld organization he was running + the conspiracy behind how he took down King Riku.
That is in no way the same as: Removal of titles for the Two ongoing warlord + a Warning that the biggest shitshow under Sakazuki's reign might just take place. Fujitora, who wants to get rid of the Warlords, decides to go there in a situation related to two warlords. And tells Doffy that he's got information that his activities have been violating the rules of the 7 warlords. This Fujitora getting information on Doffy from unknown source, absolutely nothing to do with the HQ and the false report.
Then of course he's also there for the issue of Law's warlord status, to confirm the legitimacy of the report that they've allied, thus depending on the truth Law's title would be revoked or not.
To claim "Admiral showed up for Doffy" is just insane disingenuous. An admiral showed up to a situation that involved assessing the titles of 2 warlords + a warning sent through Smoker by a former admiral who has connections with the underworld on possibly the biggest shit show to take place so far MIGHT happen.
Unless you think Kuzan was referring to rolling out ADMIRALS, not just an admiral... but all 3 of them... to take on Doflamingo lol.