I'm not defensive at all. I'm pointing out that your statement makes no sense in the way that storming Australia makes not sense when you're playing Monopoly. As such, the charge that it's a glaring omission is, well, without any weight. I'm not getting my back up, I'm pointing out that you're coming in from left field and making statements that don't really make any sense.
I asked a question, you went into a mini-rant about Monopoly and Risk. I'd call that at least a bit defensive.
Nope. I'm saying that passively investigating a murder scene where there's no dramatic interest pressing on the play is not something that PbtA even cares about.
I played GURPS for a while. That system, bless it's papery heart,
tries to include rules for wildly cinematic games, but honestly that's not a genre the system "cares about." It's really a system that wants math, not crazy stunts and high power levels. But GURPS still has rules for cinematic games, as clumsy as they are.
So:
does PbtA have rules (even if they're clumsy) that would allow for investigation, or not? And if so, what are they?
(And why would you consider investigation to be only passive? Because all of those examples I gave you have dramatic interest in them. There would be a real driving need to solve the crime before it's too late, especially if it directly affected you in some way (a loved one was killed or is a suspect; the killer has made it personal; the killer will strike again unless you stop it and you don't want any more blood on your hands).
I'm guessing that by what you continue to say, the answer is
no.
in the same way that D&D doesn't care about what it's like to be a teenaged werewolf exploring your sexuality and finding out you're deeply attracted to a same-sex vampire even though you're dating the super hot opposite sex succubus cheerleader. This seems like a glaring omission in D&D, yes?
And yet, I can actually play that out in D&D. I don't even
need rules for that sort of situation--that's pure roleplaying--but if I did want rules, D&D still has skills, subsystems, and other abilities that could be used, with a little creativity. ("I cast
augury. Will I be able to resolve my feelings for the vampire?" The spell says
weal. "Is my relationship with the succubus a healthy one?" The spell says
woe.) You want a high school drama? There's the Renown and Loyaly subsystems, right there in the DMG. Both of those would useful for high school, and the upcoming Strixhaven book likely has more such rules
and it's a school-based environment.
"ok, let's just accept it works that way, can I move my understanding around to make that work?"
Unfortunately, I can't just "accept." I need to know the whys and hows. What can I say? My parents raised me to question authority.
If the answer is, no you
can't do investigations with PbtA games unless you do it as pure RP with no mechanics, then just say that. Saying that the game "doesn't care" about it is a non-answer to me, because it's a game; it
can't "care" about anything. It either has a rule for it, or it doesn't, or it has a rule that can be used for it even though it's not the rule's primary purpose. Like the
augury I mentioned above. It's not
supposed to be used to divine one's sex life, but I'd allow it, and I'm pretty sure all of my players would as well, if they were in the GM's chair.
And, click, it locked in and I got it. I still play 5e, and don't bother with this approach at all when I do, because 5e isn't a game that supports this.
Maybe your D&D games are lacking because you haven't tried it.