Any aggression you feel was there was purely an inferrence on your part and was not intended. I have to admit however that when logic seems flawed or hidebound, that is something that frustrates me.
"Just the facts, ma'am"
"One-in-a-million chances happen nine times out of ten"
- Terry Pratchet
For a start, your appraisal of Chance feats strikes me as a classic example. Or rather, you're being blinded by the fluff of it and ignoring the mechanics. First and foremost, we're playing a game that is almost entirely predicated on random chance. Skill ranks and situational bonuses stack the odds, but the outcome is still randomly determined by the roll of a d20. Action dice -- when they aren't being used as a gatekeeper of awesome -- are a further probability-based mechanic that you use to increase your chance of success.
Chance feats are all about affecting, as you describe it, narrative probabilities. They're not about enhancing the capability of characters, per se, but about how they interact with the story. For example, take feats that generate and use edge to let you be a battlefield badass via whirlwind attacks and chi blasts. Then take the chance feat that lets you start with 2 extra edge in your pool, meaning you get to pull off that cool flashy move sooner than you would otherwise. Was your character lucky enough that they managed to find an opportunity to attack early, or were they badass enough that they had the capability to make that move before anyone more ordinary would have been able to manage?
Your example of it being a Tactics check to break an opponent's story? Good example, but remember that all the enhanced error ranges don't mean a thing unless the suspect rolls inside that range and you've got the AD to beat them. Whether that slip is expressed as a lucky break due to the arrogance of the suspect or an expression of the player character's exacting skill at interrogation successfully getting under the suspect's skin is mechanically irrelevant and down entirely to the dice falling in your favour.
I'll refer you back to my reinterpretation of the chance feats as a reflection of the character's skill rather than their in-story good fortune. Seriously, regardless of whether you happen to stumble across the clue without expecting it or were diligently pursuing an unusual angle of enquiry, on a poor roll all the skill ranks in the world won't change a feat-boosted action being the difference between showing a suspect was only in the general area of a crime along with countless others, and being able to put them at the scene of it.
- Stan Freberg
Whether they are garilous or terse, all detectives are talkers. They have to be. You certainly don't get to be a renowned inspector without the ability to get people to talk to you or likewise get your point across to them. Because sure your Inspector can be a dogged Dredd type who via an unending onslaught of intimidation will track down someone to deliver on-the-spot justice, but the class itself should be just as capable of the ability to persuade a frightened victim to give testimony without moving outside their class skill list. Not to mention that if you have Bluff on the skill list, the class is absolutely a talker class.
You can easily dump Haggle to get Impress back into the class list and leave it to the player to decide whether they invest the ranks in it instead of having to expend one of their origin skill choices. Especially as Haggle is a totally rubbish skill in Fantasy Craft and should have been much more like Spycraft's Streetwise skill.
Your listing of all the detectives capable of fighting? Basic proficiencies and fortes, the lot of them. Not a feat required. Out of all the basic combat feats, the only ones that really speak to being a detective in the classic mould are the aggro and charging chains, allowing you to provoke a suspect into hasty action or run them to ground as they try to flee.