I'm saying that absolute DM fiat, without baseline assumptions, does not serve the goals of play. The goals of play are best served when the players have reasonable expectations of what outcomes are possible. Your argument that the rules are fluid and entirely subject to DM fiat at all times does not establish a useful baseline.
"Reasonable expectations of what outcomes are possible" is achievable through understanding the context of the fictional situation without any knowledge of the rules. Someone who doesn't know the rules at all can certainly play by listening to the DM describe the environment and then saying what they want to do, knowing at a minimum that sometimes what they say they want to do will have an uncertain outcome which brings rules and dice into play at the DM's discretion.
You have no idea how I view the game, and it's certainly not like it's a previous edition. I further find it ludicrous that you think that this edition somehow empowered the DM more than previous editions did. Granted, this one makes it more obvious, but it's not special in the rule zero case.
It depends on what you mean by "Rule Zero." If you say that means that the DM can change any rule at will, I'm definitely not referring to that. As I mentioned before when it was suggested I "ignore" rules, I am not changing them, only using them as needed which is in my view how rules are treated in an RPG - largely descriptively, not prescriptively.
I do view the rules as presented as the baseline assumption of the game that my players will bring. I don't think they should be changed or viewed as fluid because that prevents the players from making rational choices based on expectations. That's not to say they can't change, or that the DM isn't responsible for making rulings when the rules fail to cover a situation, but that the DM should not be changing rules willy-nilly or on a whim. Your blanket argument that the rules serve the DM result in arbitrary enforcement of rules as a supported playstyle. Why, then, have a set of rules if your first inclination is to ignore them?
Again, players can make decisions based on what they understand of the fictional context of the situation. And I'm not suggesting changing rules "willy-nilly or on a whim" or indeed at all, nor am I saying to ignore them. In my view, they are tools to bring into play as needed. If they are not needed, they don't need to be brought into play. When they are needed is when there is uncertainty as to the outcome of a fictional action.
No, the rules establish that if you use the ability, the target makes a save. The save is a roll of the dice, not some other mechanic. There's nothing in the rules that say, "determine if the DM thinks there's conflict when you use this ability before rolling your save. Depending on that determination, anything the DM wishes may happen." You're inserting this concept of uncertainty when and where you want to to justify ignoring the rules as written. Again, you can do this, but please stop pretending that there's a 'determine if there's uncertainty' step in the PHB or DMG. That's your rule, and you apply it how you want to, and that's perfectly fine. But it's not part of the baseline rules at all.
"Sometimes, resolving a task is easy. If an adventurer wants to walk across a room and open a door, the DM might just say that the door opens and describe what lies beyond. But the door might be locked, the floor might hide a deadly trap, or some other circumstance might make it challenging for an adventurer to complete a task. In those cases, the DM decides what happens, often relying on the roll of a die to determine the results of an action."
- Basic Rules, page 3
So for example if the barbarian tries to frighten an enemy with his or her menacing presence, I can decide that this was so easy that no saving throw is necessary - it just succeeds. If there is some circumstance that might make it challenging, such as that enemy girding its will against the attempt at intimidation, then a roll of a die is called for, in this case, a saving throw.
Special pleading, again. You can't just say that 5e is exceptional in this regard as if it actually supports your position to do so. It may be special, it may support your position, but you can't get there through assertion. There's nothing in 5e that, in any way, explicitly establishes that your choices are correct. The way that Intimidating Presence works seems to contradict it, at least as far as you choosing to ignore the explicit functioning of that ability. I get that you have a mindset and a method that works for you and yours, but it is not inherently better than another's just because you think it is. Nor is it more correct. You choose to add player immunity to social abilities as you wish, but that's not inherently better than allowing those abilities to work on PCs. Nor is either position clearly supported in the rules -- they both can claim equal precedence (your ruling on Intimidating Presence, though...). You've been smug and making assumptions about how people do things at their table with the implication that if they just opened their minds and agreed with you, their games would become better. I know what you're doing, I fully understand it, I do many similar things at my table (I give my players great agency with their characters to determine things about the world and to engage as they choose), but I reject the idea that the game constructs of characters are somehow uniquely sacrosanct just because there are players behind them.
Please note I will no longer be responding to any statements that suggest I'm saying or inferring things that I've already stated are untrue, specifically, that I believe my way is "right," that others are having "badwrongfun," that anyone is a terrible person for not playing as I play, that they'd have more fun if only they saw the light, and so on. I've addressed these assertions repeatedly already and I refer anyone who wants to continue with such assertions to my previous posts on the matter. It is an unproductive line of discussion. In my view, it's focusing on tone to avoid hearing the content which I find regrettable.
At the same time, I will endeavor to double check my posts for any language that could be taken as inflammatory in the above regard. If despite my efforts, something doesn't look right, please see my comment above.
To me, if the player asks me 'I'd like to make an insight check to see if my character thinks this guy is telling the truth,' I don't see anything wrong with that because that's the player wanting to tap into the character's abilities and awareness.
If the DM decides on success, failure, or uncertainty (and ask for a roll), why would you want to ask to roll? Wouldn't you rather see if you can achieve outright success? I would never ask the DM to roll. I'd prefer not to leave my fate to the dice, if it can be avoided. It can't always be avoided, of course, due to the fictional circumstances, but I'm certainly not going to suggest there is uncertainty by asking to roll.
Now, if the DM asks for rolls for pretty much everything, then the smart play as I see it is to get really good at building characters so that I can maximize my chance of success at rolling dice, then try to limit what I do to only those things I'm good at doing. Of course, the DMG does suggest there are drawbacks to the DM asking for rolls for pretty much everything.
It seems to me that you are less willing to allow the players to tap into their character's abilities and awareness, instead preferring to leave the interaction entirely at the roleplaying level, escalating such die rolls to crucial points of conflict in the scene. I don't see much point in that, I'd prefer the decisions the players make on the information to be the crux of the scene, not the die roll to resolve uncertainty.
Not at all. Players are free to tap into their characters' abilities and awareness. They establish the fiction to do it and then I narrate the results of their actions, sometimes calling on dice to resolve uncertainty.