You're suggesting it is better that the GM cannot roleplay the NPCs he/she introduces into the game world, and when I mean roleplay, I mean free of any mechanics (i.e. die rolls). I admit I find that odd.
Fair enough. I see the roles of the GM and of NPCs, and see the nature of the GM's relationship to NPCs, as being rather different from the roles of the players and the PCs, and from the relationship between these latter things.
One obvious difference in most systems is that players are under very different constraints in allocating mechanical capabilities to their PCs than are GMs. (This comes out in your actual play example in which the players don't want to pick a fight with the giants.) But it's not the only difference.
But whether or not one likes it as an approach to RPGing, I think that gating the success of players' actions behind a GM's opinions about what a certain NPC might or might not reasonably do seems clearly to be the sort of thing the OP is wishing to avoid.
Could the FG in your game talk the PC out of wanting the shard returned i.e. the FG makes a diplomacy/persuade roll?
Which system?
4e D&D does not support NPC-to-PC social influence mechanics. Classic Traveller does for morale, but nothing else. Burning Wheel does. Marvel Herioc RP/Cortex+ Heroic does. Prince Valiant does.
isn't the DM ascribing a lower or higher DC to a roll reflecting his/her opinion on what makes good or bad fiction?
EDIT: MMI kicks in if there is 0% or less chance of success on the player's action declaration, but 1% possible success or higher is ok?
This is also a system issue. A good system, in my view, establishes ranges of DCs that I trust have been established as appropriate by a combination of mathematical analysis and play-testing.
For instance, in Classic Traveller the roll required (on 2d6) to avoid close scrutiny of documents by officials is 5+ (or 5 in 6) for a character with Admin-1, but 10+ (or 1 in 6) for a character with no Admin skill. I don't think there's any objective test for appropriate prospects of success, but that's probably getting towards the outer limits of workable DCs.
A system like 4e D&D or BW has widely varying DCs (much more so than Classic Traveller) but also has many player-side options for modifying and augmenting checks, so that the GM setting the DC is only the beginning of the process of establishing the chance of success. (This is one of the reasons I've described Classic Traveller as a
"dice-driven game".)
IMO only specific/niche game engines can get around this such as Shadow of the Demon Lord or PbtA where there is no GM determined difficulty (thought even then SotDL allows banes and boons to be added through GM discretion and I think some iterations of the PbtA game engine allow modifiers which can create the same effect)... but for the vast majority of mainstream rpg's the GM is deciding the chance that something exists even when he is letting the dice decide the outcome.
I'm not sure which "mainstream RPGs" you have in mind but Classic Traveller is not that obscure and has a very wide variety of subsystems that set DCs for various action declarations. In my current campaign we've resolved: dealing with bureaucracy and with police: assaulting a base on foot; assaulting a base from vehicles; starship combat; small group combat; starship infiltration; EVAs; tracking down a satellite in orbit; curing disease; searching for the Psionics Institute; evading orbital fire in ATVs; hacking computers; engaging in interstellar travel and interstellar trade; seducing an agent to obtain information; and seeking something out on the surface of an alien world. Maybe other stuff as well I'm not recalling at present. The only one which didn't have a workable mechanic for resolving the action, either expressly provided or easily extrapolated from what has been provided, was the last one. Which is a pity, because exploring alien worlds is an important aspect of sci-fi play.
I've already mentioned how BW and 4e handle the issue of establishing odds of success. In the case of MHRP/Cortex+ Heroic, every check is an opposed one, and the system has elaborate rules for establishing and maintaining the Doom Pool which is the default source of opposition if nothing else applies.
Prince Valiant plays somewhat between Traveller and Cortex+ Heroic in this respect - many checks are opposed; where they are not, the system for setting DCs compared to the system for determining the size of player dice pools tends to mean that initial chances are rarely less than 1 in 4 (ie 2 successes on 2 dice), although the complex resolution system can exhibit a death-spiral effect, which is a reason to use it with caution.
Perhaps all the systems I play count as "specific/niche game engines"?
Ah, you mean without forcing players to provide further details for their action declarations so as DMs we can adjudicate the likely chance of success. Such Bad DMs.
I don't think that [MENTION=85870]innerdude[/MENTION] has even indicated what system he is playing, let alone how action declarations work in that system, so I'm not really sure what you're getting at here.
Eric: I try get my shard back from the Frost Giant without starting a fight.
DM: How do you go about that, she has already placed it back in her hair?
Eric: I use diplomacy, I'm proficient.
DM: Cool, what do you say to her?
Eric: Well, I ask nicely, smile a lot and bow often?
DM: Is there something specific that you say?
Eric: Nah, I have a +7 on my Diplomacy roll. My character is really good at persuading people.
Matt: Yeah, but this is a giant, a Frost Giant, who has recently been annoyed with humans for lying to her and her kin. They've been sent on a wild goose-chase, we are lucky they don't kill us.
Eric: All the same, besides who cares about that backstory. My character is a really good talker.
DM sets the DC, Eric rolls a 25 after modifiers.
Eric: I roleplayed the crap out of that!
Liz: You sure did E. (They high-five each other and then, picks up her dice and turns to the DM) I also want to roleplay.
Are you posting an account of how it happened at your table? All my discussion is taking for granted that the people at the table are interested in playing the system that is being used, including making action declarations in the way the system expects.