Yeah this works. It's weird to think that someone so old would be vulnerable to the "Saturday morning cartoon villain blabs about his evil plan and gets thwarted because of it" trope but it happens repeatedly where the Denarians are concerned.
Then again old doesn't necessarily mean wise.
[X] Plan Poison Tongue
In my opinion there's probably a couple factors
1) Arrogance
The kind of person who actively hooks up as the junior partner of a Fallen Angel, one of the eldritch terrors of the world setting , kinda has to have arrogance as a foundational trait. Hit the right buttons on that personality type, and they will often show off how much better they are than you.
And its not just Denarians.
Remember Nfested!Maeve monologuing after capturing Dresden in Cold Days? Or Lord Raith doing the same thing?
Or Shagnasty?
2) Recruitment
The Bad Guys are always in the market for high-quality recruits and talking to them. Nicodemus spends significant effort trying to recruit Harry, and we see Lartessa put some effort into trying to talk him into changing his mind with sexual wiles.
Even the Walkers spend a lot of time monologuing; He Who Walks Behind monologued at Harry both when he was 16, and when he met him again in Blood Rites. He Who Walks Before tried to
recruit Harry after he thought he'd defeated him in Cold Days, and He Who Walks Behind had a fairly long convo with Harry in Battle Grounds while possessing Justine.
They all talk, if given the opportunity.
3)Loneliness
The Bad Guy life doesnt really promote much of a community of peers. You have minions and if you're junior, bosses.
Not really many peers you can talk to, and not worry about it being used against you.
The Good Guys at least are known dangers who can only kill you, and its a lot safer to talk to them, and then kill them when you're done.
Remember, its not usually enough to win for these guys.
Its also as important to crush and humiliate their enemy, and have said enemy know it.
Even usually competent bad guys like Nicodemus will backslide under stress, like when he went after Michael's family in Skin Game, captured Charity, and then waited to make an entire show of killing her instead of simply having someone cap her as soon as they caught her.
I think the only bad guys we didnt see monologue in canon were Cowl and Peabody.
And the Outsider cultsis in Thomas' short story and Molly's short story.
Everyone else has given a long speech of gloating or personal justification.