Hello Milkfred, and thank you for detailing your issues. I think that a lot of this is going to boil down to "YMMV", but I'll throw my 2 gold into the ring.
1. Skill Checks are Boring
BG3's skill checks have a problem - they, without fail, feel like they fit the mould of succeed or fail. With success meaning you do the thing you wanted to do and fail meaning you don't, and often end up in a fight.
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And you don't even get experience for making the skill checks either.
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Oh, and the fact that so many of them are just DC10 (aka coin toss) is another related problem. I assume a lot of the numbers can and will be changed, but the underlying structural issue of it not being fun or interesting to fail is a deeper problem.
To take your sub points one by one.
Any given roll of the dice can be "boring"; I think that it's about context. And depending on the game, there can be a TON of "things to roll for" (say.. Harnmaster) or very generic/few types of rolls (FUDGE/FATE).
As for "experience" it's not from any roll of the dice, no matter what for; skill check/saving throw/attack roll, rather it is from the sum total of the interaction "defeat" or "success" regarding the encounter. The fact that in an online setting it's much harder to give experience for "dealing with" or "negotiating" rather than bypassing, is an inherent system problem. I'm not sure how to get past that.
Target number "coin toss"; I disagree, as there have been quite a few skill checks for me so far that had 6, 4 or even in two cases 1 as the target. Reminds me of tabletop when the CHARACTER has the skill and the PLAYER is being a jerk, and the DM sets up a roll, because "the character can probably do this" but because of jerkiness, lets just check and see if Karma wants to F you up. (oh for the sake of things I will throw in that our convention is that all "known" rolls are made visibly so you will know if you succeeded). There are some rolls that the DM makes, and some so subtly that the players will never know what they don't know....but more on that later.
2. Story Elements are Missing/The Rest Mechanic
The first time I went to camp, a demon showed up and I felt like I'd missed a few pages. So, on my second playthrough, I made it a habit to go to camp whenever a party member talked about being tired. This improved a lot of things by a drastic amount, and smoothed over a lot of initial issues I'd had with the plot and characters. I feel like Larian may add in a fatigue mechanic at some point, but this is a pretty drastic issue.
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At a certain point, Lae'zel mentions that you should be careful about going around and telling people you have a worm in your brain. But this had come after Nettie had already tried to kill me. If the player has been told that, hey, maybe don't go around telling people you're going to turn into a Mind Flayer, it might alleviate the issue that someone tries to kill them over it.
I really like the rest mechanic, but <snippage> But without any sort of mechanic, how often should I be going to rest? And what am I missing if I don't?
To the first point (should we talk about the worm in our brains); right away off the ship the first encounter kind of tells you that individuals will not react positively when they think you are in any way part of/tainted by/whatever by a Mind Flayer. Since that encounter is pretty hard to miss (and granted, I've been known to miss things more obvious) it's reasonable to suspect that's an important thing to keep in mind.
As for the rest mechanic....I've been frustrated because it's severely bugged in our multiplayer games, but you had mentioned that by resting when various NPCs mentioned they were tired, things were better. So there is an in game cue of sorts.
3. Players Want to Experience Everything
A solution to the Nettie thing is to just not talk to her. But players generally want to experience all the content they can in a single playthrough. Having a consequence be 'you just don't get to do something' is related to my first point. I'd put a few other things under this umbrella - like Perception checks as you're exploring - as being similarly annoying. What did I miss? Who knows, but now I have this feeling in the back of my head that I'm missing out on something. Was it something that I'd think was cool? A neat bit of lore? Something to make Lae'zel like me? I can tell myself that it was probably just two gold pieces and a fork, but my brain will insist otherwise.
Had to quote your whole thing here because it's cool and well written. However this points out (yet again) one of the difficulties in playing with a computer as a GM is that the programmers have to decide if the "background rolls" are going to be done in a wya that the player knows...or just "in the background."
I like the use of stat checks... when my bestie's Wizard looked at the control panel on the ship, she could figure out some of what it could do. When my Ranger took a look, it was a bunch of random buttons. That makes SENSE to me and I like it.
4. Gameplay and 'Choices'
Players draw a distinction between choices in dialogue and choices in gameplay.
????? how is dialogue NOT part of gameplay, ESPECIALLY when describing a game as a "role playing game".
Going into combat with Nettie to get the antidote is not seen as a 'choice.'
It is a choice. It is ALSO the result of previous choices made by the various characters. In a battle the "killing blow" does not somehow invalidate that there was a battle, that there may have been words or threats before the battle and there will be consequences after it. I will say that I did NOT kill Nettie and my character did have some very interesting consequences to that set of choices.
4. Stat/Class (Im)Balance
The fact that Charisma controls all of the 'roleplaying' skills is pretty much absurd. I understand that it's how the 5e system is, but that's my point - the system sucks when it's being run by a machine.
Two points:
First "controls" is not accurate as persuasion also plays a role
Second it's no more absurd than using strength to determine damage bonuses, or using dexterity to adjust stealth. The point of having stats is that they mean something.
5. Modifiers are Boring
Pretty self-explanatory. The player gets +x on the dice roll based on their stats and/or proficiency bonus. Yawn.
Where are the circumstantial bonuses? Where's the character, where's the history?
Ahem... the first sentence above is the answer to your questions below. Proficiencies, stats, all of that is inherently part of your character and their history. This is why I prefer to create characters rather than use pre-made ones; I'm CHOOSING the skills, the background, the class to reflect history and experience.
6. Combat Downgrade
Move/Standard Action/Free Action is a step down from Divinity: Original Sin 2's AP-oriented combat system. BG3's combat is perfectly fine, but it's also not nearly as interesting. Again, the issue is that BG3 is doing it as close to tabletop as possible.
So what you are saying is that tabletop gaming is tricky to translate into an online game.
I think we can all agree on that.
OH and one last thing you said caught my attention:
missing loot from shoving people into pits.
Climb down and get it then. Or don't, and don't get it. How is it in the realm of any sort of believeability to "get loot" unless you actually get it. Unless you are playing Shadowrun or Cyberpunk and you are putting the body in a pit before you hack their savings accounts and steal all their cred. But that's a way different game.