Here I have to point out that I'm a computer programmer, and I choose my words carefully.
Feel free to write assertions in C++ if you think it would help.
believe I wrote that you can't create a "mechanically interesting" class without mechanics; this is not to be confused with saying that you can't create a class that has advantage on every skill used in investigation, but rather a value judgment that such a class doesn't meet my threshold for "interesting."
I think the misunderstanding is coming from the vague idea "mechanics". We have agreed that they are out there, but we haven't really spoken on what they are like. This would be easier if we had a common frame of reference. I don't know that we do, but suppose we are building an RPG and we are tasked to defining RPG subsystems. The architect would like us to build supplemental systems that would allow the game to be played in different ways that aren't well supported by the core game and its turn based tactical wargaming core. One of us might be building a 'Mass Combat' subsystem. Someone else might be building a 'Evasion/Pursuit' subsystem. Someone else might be building a subsystem for handling Stealth or Long Distance Travel.
Now, there are several ways to go about this. There is no reason why each of the subsystems would have to use the same rules. Each of us could build systems for running each of the different aspects of the game that were self-contained, and we could just transition between games during scenes. I suspect a lot of cRPGs work like this. Think about Mass Effect II and how there were specific 'combat zones' and specific dialogue interfaces that didn't really interact with other parts of the game. And that's fine, and maybe our hypothetical Mystery/Investigation subsystem works like that. We flip to it and it self-documents what characters from the main game can do.
But, it's also possible that the main game's core resolution components and fortune mechanics are integrated into each subsystem. That is, the 'Evasion/Pursuit' subsystem instead of having its own unique components might have all the values derived from or shared with the core game. All the subsystems might rely on a D20 style mechanic. Your athletics skill bonus in the main game is used to resolve an 'Evade Obstacle' test in the evasion/pursuit subsystem. Your tactical movement rate might directly impact your bonus in opposed 'Pulling Away/Closing the Distance' checks. If you make a 'Break Away' maneuver, it depends on your Acrobatics, Ride, or Handle Animal skill depending on whether you are on foot, mounted, or controlling a vehicle. And so on and so forth.
The architect could have looked ahead at this and said, "I want this class to be particularly good at 'Running Away'" and foreseen how various character components and abilities could be reused in different subsystems. When a game master makes the decision then to switch to a new subsystem, he calls then for the exact same familiar tests that the player is already used to making. The only difference is that the player's propositions get resolved by a different underlying engine. Instead of moving a figure on a grid map a fixed distance to 'chase' an opponent in what (if the goal is pursuit or evasion) would be a dull straight forward (disassociated) mechanic were player's characters froze in place while someone chased them and the range opened up and closed incongruously, we would be using an abstract continuous (associated) system where we tracked only the relative distance between a group of moving entities and adjusted it according to opposed tests and different actions that the character's undertook.
So we have mechanics there that are exciting and appropriate to the scenario we are imagining that don't interfere with our imagining it and make the outcome tense, exciting, and doubtful in the way using the tactical wargame to resolve pursuit/evasion wouldn't be.
But we don't actually need separate character abilities on the character sheet to interact with that subsystem. If we knew ahead that we wanted a mystery subsystem, we could have some broad skills like Insight, Observation, Research, Bluff, and so forth and call out our intended 'skilled investigator' class as being advantaged in those things in various ways.
So yes, I think we have to build the subsystem before we can expect the average table to be able to play that part of the game well (because rulesmithing is hard). But I don't think it necessarily requires the subsystem to interface with a character at a level beyond things like, "You have advantage on Insight and Observation checks." or "You may make Observation rolls as a Free Action without a penalty" or "You have a number of Focus points equal to your class level. Before rolling an Insight or Observation check, you may spend a focus points to set the result of your roll to '20'. Replenish your Focus tokens after a long rest." or "Library research takes you only half the usual amount of time." or whatever.
I don't understand how that is inherently not interesting. I mean fundamentally, that's the sort of things that 3e feats or 5e class abilities do with characters interacting with the combat subsystem. It's interesting to the extent the combat subsystem is interesting, and boring if the subsystem is boring.
I wouldn't mind making room for Sherlock Holmes, but I think the way I would choose to do it is by inventing new affordances first (i.e. rules for solving mysteries), and then write the character class in terms of those affordances. I think there isn't any reason you couldn't introduce the notions of Scenes, Find a Clue, and Noticing clues into D&D--the example I gave was intended to still be in the D&D genre.
Yeah, but there is also no reason why or GUMSHOE inspired subsystem could define its interactions in terms of the core character abilities. For example, we might right something like this, "If the character is Proficient in Perception, he always notices a Hidden clue any time he investigates the area where the Hidden clue is found." or "If the character is Proficient in Research, he always discovers a Library clue any time he researches an archive where the clue might be found." or "If the character is Proficient in Bluff, he always discovers a Rumor clue any time he seeks rumors in an appropriate location."
When I suggest creating rules for things like Find a Clue/Solve a Scene, it is in the context of offering more affordances to the players at the metagame level, so they know what kinds of action declarations make sense. It doesn't mean that action resolution has to get new rules.
I'm of the opinion that a player might benefit from knowing the rules, but that knowledge of the rules should not be necessary. A player doesn't have to know that in the rules "Run Down Rumors" is a thing, to suggest that they go to the pub, buy some locals a drink under some pretense, and after a while try to get them to talk about something with a leading conversation.
A Sherlock would be able to make an intuitive leap to receive this information as soon as he acquired three Clues, instead of four.
Alternatively, a Sherlock wouldn't even need to roll to Notice a Clue. He just would - no chance of failure (because he's proficient in Perception, Investigation, and Linguistics, and our rules tell us that Clues are automatically found by characters proficient in the relevant skill, bypassing the fortune mechanic). This would simply require the subsystem to reference the rules, rather than the rules to reference the subsystem. Likewise, alternatively, according to the rules of clues anyone when finding a clue could spend a Focus point to, after noticing a clue, to receive the gist of a from a location he's not yet visited, or to intuitively know the location of another clue. The Sherlock, being vastly more equipped with Focus tokens than other classes, is best able to interface with those rules. And the nice thing here is that a DM doesn't even have to have our Mystery/Investigation supplement or want to use it. It won't be cluttering up his game if he wants to run hack and slash. And the player of the Sherlock will have things to do with his abilities even if he doesn't find himself in a Mystery game where he shines the most, or will shine even if the GM decides that the mystery here is too simple to justify a full fledged Mystery Scenario and just asks for an Observation check.