Negotiation and Investigation are things that players and GM can actually do themselves. Tell the GM what your character wants to say, and tell the GM how your character is looking for clues. And the GM can determine success or failure based on reasoning and judging the situation alone.
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Many, if not most people totally don't see it that way, but I consider AD&D to be one of the best games for roleplaying and investigation, because it has no rules for it. I don't need any rules that tell me "the king denies your request, even though you made very good points and it would be in his best interest" or in which a player says "I search the room. I got a 17." When negotiating and investigating gets outsourced to a minigame, players are no longer incentived to think about how they would attempt to solve something. All they need is to declare their goal, and in a worst case scenario, any additional elaboration they make on their characters actions doesn't affect the outcome at all.
Yes, you can roleplay with every system. But some systems have "don't bother, it doesn't affect the outcome" written between the lines everywhere.
There are very different views in this regard. Some people want to play an agile Rogue or a mighty Warrior, even though they lack those traits (agility; strength; etc.) in real life. The game allows them to play the character they envision by providing rules for this.
A social wallflower may want to play a suave ladies' man or a cunning con man. A player not good with puzzles may want to play Sherlock Holmes. Mechanics for social interaction and investigation, respectively, permit the player to do so. Why should that not be permitted? If the player's oratorical skills, glibness or investigative skills determine success in these areas, then the player can only play his own skills, not those of the fictional character he envisions.
Then we get to "role playing". Your comments seem to imply role playing can only happen out of combat. I disagree. If my character loathes Goblins, this should be role pla yed - in combat, that means focusing my attacks on those vile Goblins. If my character is a wisecracking swashbuckler, then he will play in combat very differently from a grim, methodical avenger or a physical coward. That's "role playing".
Investigation? If my character has a 6 WIS and a 7 INT, portraying him as Sherlock Holmes deftly seeking out the subtle clues isn't playing that role. Nor is my 8 CHA character with no social skills played as a great orator and persuader role playing my character. It's role playing a character very different from the one I created.
Does that mean players have no ability to influence their odds? To the same extent, I suppose, that they have no ability to influence their success in combat. Casting the wrong spells, using an inappropriate weapon, attacking the wrong target, choosing the right maneuvers, teamwork to flank the enemy, or just concentrating missile fire on one opponent to reduce the opposition rather than spreading it out to lightly wound all of them are all decisions players can make that impact combat. They don't grant the characters any new abilities, or make it more likely the 8 STR Wizard's dagger will hit more regularly and more potently than the 19 STR Barbarian's War Axe. Player choices and character abilities combine to generate the combat narrative and results.
Similarly, interaction doesn't just mean rolling the dice. Do we do some homework on the King beforehand, perhaps approaching others who have contact with him, determine he fancies himself an expert in, and patron of, the arts, learning that he considers himself a man of peace, not of battle, etc. and tailor our approach to that knowledge - perhaps bringing him a gift such as an original manuscript of a famed playwright (maybe we found one in the dungeon and thought "what's this good for?" but haven't sold it yet) or leverage connections we have made with members of the local arts community, and tailoring our discussion not to the War against Evil, but the need to quickly and decisively end the raids and bring peace to the Hillsfolk. That's all tactics of social interaction, and we should gain bonuses.
Now, enough of those good points would stack enough bonuses that something already in the King's best interests (not a high difficulty for success) is guaranteed, just like a lone goblin isn't much of a threat to our party of 8th level characters. But neither are the stuff of the epic quests of Heroes - they're just easily overcome speedbumps. Tipping the balance of the war by persuading the isolationist, traditionally neutral nation to add its considerable resources to our side - allying with a side for the first time in hundreds of years? That's the stuff great games are made of. But it's also not likely to be a sure thing, and I want the pitch made by our 18 CHA orator and diplomat, not Crass the Cussing, 6 CHA Barbarian with the sole social skill of "do what I say or I'll thump ya". And I don't find it great role playing for Crass to suddenly take on the oratorical skills of a consummate politician because, today, that would be better than his usual personality and skill set.
), but, the presence of rules works to channel player actions.
