My issue - and as a player I'm every bit as guilty of doing this as anyone else, so not pointing fingers - with exploring a character's perspective and story is that it's almost only ever relevant to that character's player; which means any table time spent on its development is time not being spent on the party as a whole.
Doing this stuff one-on-one with the DM during the week? Sure, all day long. Trying to do it during the session? In general, let's not.
I'll step in here for a moment. Not always, but I'd say the majority of the time, I'm just as invested in the stories of the rest of the party as I am in my own.
Just for an example, I've got a play-by-post game that is actively running and that we end up split off and doing our own things fairly regularly. At the moment one character is talking to her evil reflection and trying to resolve her upbringing as a cleric of Light with her nature as an infernal being. I'm loving every minute of it. Another character is soon planning on giving a wish (we each got one) to their patron, which could be all sorts of massive shenangins, I'm eating it up. Another player is dealing with relationship issues and struggling with balancing her orc and human instincts.
Sure, it isn't all the time, and some people's stories end up being things I don't care about. But, I can just as easily get invested in the story they are crafting with the DM and be a spectator as I am with my own stories. Maybe I'm just weird that way, but I know I'm not the only one.
I suppose much of the time as a player I play more for the here-and-now, and let the big-picture story take care of itself (in part because half the time I'm not even sure what the big-picture story is or which part of it we're dealing with!).
Sure, each individual adventure has its own story - here we're rescuing refugees, there we're destroying a nasty temple, etc. - but that to me is here-and-now stuff, in a campaign that spans literally decades in real time and has built up maybe a dozen of sometimes-interweaving big-picture story arcs.
For me, ignoring the bigger picture story is... I don't think I could. I'm always trying to keep our context and the larger story in mind. I love that stuff. Now, I've never been in a decades long game, longest single campaign I think I was ever in was probably three years, so maybe it ends up coming down to game play pressures.
Actually, thinking about this more, this would explain a lot about how you don't seem to grok the pressures I'm talking about. And individual adventure that in no way ties to the larger plot is mostly a distraction to me, a filler just taking up space. It could be a fun filler, or not, but I always feel an urge to get us back on track.
While I know there's variant RPGs where that's the norm, I'm not sure how well it works in practice.
It probably wouldn't. So, just because the character doesn't know a numerical score doesn't mean the player shouldn't. So, why should a player not know the DCs to shatter these crystals? What is the value of keeping this information from them? Yeah, their character doesn't see a big red 17 etched into the crystal, but I'm not asking about the character, I'm asking about the player.
Which flies in the face of viewing and interacting with the setting through the eyes of your character. Some numbers, such as stats, serve as player-side informers as to how in general your character would perceive itself and-or be perceived by others. Other numbers, such as DCs, do nothing but hard-code things that in the characters' view would (nearly always) not be anywhere near so cut-and-dried. No need for the players to see those.
I disagree. The players seeing some of those numbers gives them more information to use to make decisions. It allows them to feel like they have more of a handle on the choices they are making, because they are making them with intentionality. The character doesn't need to know if the risk is relatively low or relatively high, it is a risk of death, it doesn't matter if it is high or low, you take precautions because you don't want to die. But the player can make a slightly more informed decision based on that information, rather than just having to guess.
As an example, the chance of you being struck by lightning and killed is 0.0065% , it is insanely low, probably the equivalent of rolling three 1's in a row. And yet, you probably don't go dancing outside during thunderstorms. But, if you needed to make a run to a shed to grab something during a thunderstorm... you might, because the chances of injury are very low. But knowing the chances doesn't change your actions that much. Even if it does let you make a more informed decision.
"Which way does the door open?" is an easy enough question to ask if the DM forgets to tell you; not just push or pull but which side the handle/hinges are on, which can make a difference if characters want to line up their weapon-hand or shield-hand closer to the opening side. (amusing side note: one famous old-school module notes in its default description for dungeon doors that the handle and hinges are always on the left, which read literally means doors in that dungeon are mighty hard to open...)
Why would the DM have to tell us? Does it really matter that much? To the point that if we don't hear if the door pulls open or pushes open we should stop the game and ask? This was literally the only time in nearly ten years that a door being pushed or pulled ever mattered, and it was because the DM wanted to laugh at us for saying the wrong word and looking like fools.
Also, what do you mean their weapon-hand or shield-hand? That isn't a thing in DnD 5e, we don't specify the handedness of our characters. I've never told the DM once which hand I was holding something in, because it never mattered.
Ye-es, I see on reading it that 5e has taken out the strength-of-enchantment piece. Another dubious nerf.
And I think highlighting a major hurdle in our discussion, there are a lot of assumptions of how things "should work" or "have always worked" that are not true in DnD 5e.
Thing is, whenever someone suggests changing the rules as a fix you jump on that too.
Can't have it both ways.
I'm not trying to have it both ways. I'm trying to highlight that running the game as written we have a lot of problems that the game as written doesn't have solutions for.
So yes, if you want to change the rules, you can, but that doesn't help anyone who buys the books and doesn't buy a pack of your homebrew rule supplements that solve all the problems in the rules. And, for a lot of us, it is clear that this pillar is sorely lacking.
I'm kind of sick of having this poison pill choice. Either there is no problem with the rules, it is with me. Or there is a problem with the rules, and I should stop being lazy and fix the rules myself, because it doesn't matter if the rules are bad if I put on my game designer hat and fix them.
RPGs are the only gaming in the world where poor game design seems to not matter, because the answer is always for the players to act as game designers.