That's only a good idea if they are going to be in constant contact with other wardens. In practice, the North American wardens have months to years where they rarely see one another. They have plenty of time to train in methods to avoid detection and recruit followers. Harry sees more major magical action than any other warden besides Morgan and they still think he had the free time to build his plot for world domination.
And yes, I can see that plot:
Get raised as a warlock by Justin, rebel and kill him in "self-defense".
Bob, otherwise known as the Word of Kemmler.
Take advantage of your grandfather's mercy and get trained further. Earn the trust of several Senior Council members.
Work with local law enforcement and organized crime to build contacts.
Form an alliance with the White Court and later the Winter Court.
Help overthrow the power structure of the White Court while forging "relations" with the new leaders.
Stop the heirs of Kemmler. You're not ready to advance your plans and it'll build more favor with the Senior Council.
Go to war with the Red Court with the support of the Council, Winter and the White Court emerging victorious as the new Winter Knight.
Take down the Formor and openly marry the Queen of the White Court.
Out of context it all holds together but it leaves out some things that don't add up to evil incarnate rising:
Stopping the Denarians at multiple points while resisting their efforts to recruit you, including actual coin possession.
Having KotC show up to aid rather than oppose you on multiple occasions and being ally, mentor, houseguest, baby-sitter (Molly) and drinking buddy with each of the KotC that served since you've been a wizard.
Getting Soulfire from an Archangel.
Actually, telling the Council about most of these things openly with the exceptions of Bob, the Coin and Soulfire.
It's easier to just jump to a general conclusion and summary judgement than put in the work of investigating. Just approaching Michael and asking him to address some areas of concern would get most of this. Unless they think Harry has convinced a KotC to lie for him.
Part pf Harry's problem with the WC is an Image issue. From the average WV members perspective Harry only shows up to meetings that are generally about bad news.
Harry is a young wizard who should be kissing the rings of older members, trying to make friends and networking. Instead he shows up to meetings late, in the wrong attire and with the attitude that the Council is beneath him. Harry shows up on the WC worst days delivering bad news and expects the WC to back him up.
Image Harry as a core worker, Dude got the job based on friendship with the manager, skips meetings, shows up to criticize the work you have done, claims he can do better than you idiots.
Goes away for who knows how long. Breaks the rules ,is saved by senior management , wants your help with a project he messed up, and you are ordered to help him. Dude f***s off to who knows where. Comes back barely contributes. And then when the project seems like its doomed to fail, shows up with a brilliant solution and gets all the credit. That's Harry from the Average WC member
All anyone knows about Harry is that he is trouble. Harry makes the barest amount of effort to make friends with members of the WC