I have played with many groups and many players, and most, myself included, have one thing in common: they think they know a lot more about the world, their characters, and the campaign in general than they really do, and most of the assumptions players make are generally at least partially wrong. This has really only lessened when I've managed to play with the same people routinely for long periods of time, and even then, it can be surprising what assumptions others are bringing to the table. Usually the moments when those assumptions are most likely to come into play is precisely the moments that you are advocating leaving everything up to the player. This causes a lot of stress at a lot of tables. This is where using some of those mechanics on the PCs can help, if used right. You don't tell them them, "You're intimidated, take a -2 to all rolls for the rest of the encounter," you tell them "you are intimidated because (flesh out world or character history here to give them something to work off of), take a -2 to all rolls for the rest of the encounter."
Why does it cause the table stress?
Acting on bad assumptions is the fault of the player in my view and thus correctable by the player by taking whatever action is necessary to confirm those assumptions before acting on them. If the DM describes Beat Horsedeath's attempt to intimidate the PCs into surrendering and the Horsedeath clan is known far and wide as brutal warriors not to be trifled with and the player has forgotten or ignored this, that is not the DM's problem as far as I'm concerned. The player is welcome to say "I try to recall what I know about orcs of the Horsedeath clan..." or "I want to size up this warrior to see if I can take him in a fight." These are actions the DM can adjudicate.
Of course, there is potentially some culpability on the part of the DM. If the DM did not inform the players of this knowledge while framing the scene (or otherwise imparted the information in some other scene), then the player cannot be expected to make an informed decisions. However, that still doesn't stop the player from trying to confirm his or her assumptions. That's just smart play in my view. Don't assume every troll is harmed by fire, after all, because the DM
can change up monsters.
Inspiration is a great idea, but generally requires the player to actually understand enough about the world, character background (i.e. what does being a noble of the city of Israth really mean?), how they fit in the world (do they agree with the general behavior of a noble of Israth or do they deliberately do something different?), etc. before that mechanic can really have full effect.
Not really. At a minimum, they only need to play to their established personality traits, ideals, bonds, and flaws which they themselves choose as part of their background selection. If you want to award Inspiration for knowing particular things about your campaign setting, that's just a bonus.
Short of sitting everyone down and giving a long explanation or writing it all out, and hoping they take the time to read it, the moments where any of the skills can potentially be used are the only real chances a DM has to actually get across enough of this information for player choice and inspiration to really work.
The DM can do this through describing the environment, framing things in terms of what characters in that world would know about the elements of that scene e.g. nobles of Israth. No mechanics are required in my view.
It sounds like your group can do this without a lot of heavy reliance on mechanics; most groups aren't that lucky.
All groups can do this in my experience. I run a lot of pickup groups on Roll20 and it doesn't seem to be a struggle for anybody.
Most groups I've been in, that really doesn't happen; some or all of the players would play off the intimidation as a failed attempt, the scene largely ends up being a largely blah encounter, and the game suffers. There really does have to be some kind of mechanical oomph behind the perceived negative as most players will not touch anything that leaves them less than 100% total control, and therefore, never really grow either themselves as a player or their characters.
I don't see why this must be necessarily so. Beat Horsedeath makes his threats. Maybe the PCs respond with threats of their own or the more cowardly characters advise caution. Perhaps they call Beat's bluff - or maybe Beat's a badass and proves it. Lots of potential in an interaction like this that doesn't involve rolling an Intimidate check for Beat against a PC and then telling the player his or her character is "intimidated."
It's the same reason that most negative stats tend to be downplayed by the majority of players. Any kind of exposure or weakness in the character is actively and quickly tamped down, leaving little room for the DM to expand the story, world, or characters beyond what the players currently know (or think they know) without a lot of force. Much of this is well earned on the player's part, as many have had bad experiences with DMs that went overboard, but ignoring the mechanics completely isn't going to resolve any bad experiences.
Again, I don't see the connection between downplaying low stats and the DM being unable to expand the story or setting. (The characters becoming developed is on the players.)
In the end, for those lucky enough to find a consistent group to play with, simply ignoring or choosing to not apply rules is a perfectly valid option because it can be done in a larger framework of trust and common understanding of what the game should do. For most, it isn't; sporadic and selective use of the rules when trust and common understanding is not already present, as it won't be in most pick up groups or organized play setting, actually makes things harder, not easier. Trust and common ground only come with consistency, and folks willing to bend the skills rules so far as to not apply them to PCs are generally also going to make other changes to the game that newcomers are not likely to fully understand and immediately appreciate. There's a reason I won't play 5E with just anyone, or for that matter, any organized play league now that I have other options; too much potential table variance makes it hard for me to understand precisely what I can reasonably expect in most cases. So, while your approach probably works fine for your table, it would absolutely collapse at many others. This is both the strength and weakness of 5E's making the DM the center of the game.
From my perspective, I'm not "bending" the rules. I see nothing in the rules that indicates the DM may say how a character thinks or acts.
And my experience with pickup groups appears to be the opposite.
