I’m going to regret this post, but there it is.
Please use charitable reading, as I am expressing personal opinions meant with the most positive of intentions 
This is what baffles me. I agree. But I can’t honestly figure out why things are like they are. Or rather, I have an opinion about that, but I’m afraid it is mostly critical of OSR idiosyncrasies than anything else 
If we consider as “OSR” only what this nice article explains ( LINK ) then there is no possible dialogue. OSR is the production of new material for old D&D rulesets. Period.
If instead we go past that… into the “OSR” that is open to modifying or reinventing those original rulesets, and even flat out creating new originals that aim at the Classic play experience without necessarily sticking to the Classic designs… then yes, there could and should be A LOT of cross-pollination.
Especially with the young NSR 
But here is where the cultural problems come into play, in my opinion 
Modern rpg design (I can’t bear myself to call it storygame design, considering that “stories” are a minimal part of the whole picture) is simply about designing rules that represent, as best they can, what really happens at the table.
This way, when you use those rules, the play experience that happens at the table is the one promised by the game. And vice versa, the closer play activity sticks to the rules as written, the better it will produce the play experience everyone expects and hopes for.
For this reason, the focus of the rules, the thing they describe and model, has shifted away from the impossible task of representing directly all of the imaginable diegetic minutiae (the idea that “rules can’t cover everything” is correct) to instead explain and model the real actions and interactions among Players… with only marginal attention to some diegetic minutiae if and when they are of particular importance to achieve some specific game effect, some specific play experience.
Also, one basic concept is that human brains are quite crappy at judging odds and probabilities, especially when personal interests are involved, while they are exceedingly good at judging what feels reasonable and sensible. So rules should focus on handling the first (resolving conflicts) while letting people freely do what they do best naturally, only interfering to achieve a specific effect (promoting a certain kind of fiction rather than another).
The problem is, we are all talking about “rules”, but truly we are talking about quite different concepts.
CONTENT WARNING
I am going to express pretty critical opinions about how I see the current situation with the RPG Cultures. They are my personal, albeit informed, opinions. I’m happy to discuss about them. And to change them.
-
OSR and Trad games say “rules” and think about the die size to roll on an attack. Or the “stats” they need in order to measure any given diegetic minutia they care to list into the rulebook.
-
At the same time they refuse to consider GM/Player behaviour. It is a sin to teach people how to play a specific game. But this is necessary knowledge, which ends up being provided by “the culture”.
Interestingly Classic and therefore OSR culture (and, guess what, FKR) have super strict cultural dictats and traditions. A whole rulebook of quite inflexible rules that determine if you are for real or just a n00b poser that is having “wrong fun” … but hey, as long as they are unwritten, we are happy to have them. So we can still crap on how “rules” are obstacle to play
-
Modern games say “rules” and think about how GM and Players should behave, and then which mechanics can trick them into doing exactly that, as effortlessly and with as much satisfaction as possible. This can, among many other things, also mean thinking about which die to roll for an attack.
This sends me crawling up a wall when considering how, actually, Classic designs had many elements in common with the Modern approach!
Classic designs were too new. RPGs were still finding their own identity, a bit wargames, a bit narration, a bit whatever else they might be. There was no “culture” about how to write rules for a non-hardcore audience. So some stuff is unclear. A lot of other stuff was not made explicit because of course people in the know didn’t need it to be spelled out. And some were maybe just botched experiments, or unwieldy formulations, etc.
But some seeds where there!
Consider some examples…
The Classic rules giving XPs for Gold. XP for cash? It’s unrelated! It’s unrealistic!
Yes, from a diegetic point of view that may be the case.
But the point was not to be realistic at all costs.
The point was to manipulate Player behaviour by rewarding the activities the designer deemed more important and desirable for active play to match their vision of how the game should be.
This is effing Modern, if you ask me 
And again, the whole existence of clearly defined procedures to run dungeon explorations. Have a look at this video by Questing Beast ( LINK ).
One detail among many: dungeon doors will always close after Players pass them, unless specific resources are spent to prevent it. While at the same time doors will always be open for all dungeon dwellers, be they monsters, animals or people.
Unrealistic!
Yes, but “WHO CARES?!” … these mechanics are effective at shaping the table experience of a dungeon crawl in the way the designer wants, so they are in the rulebook.
Not all are perfect, not all are effective, today we can surely come up with better ways to achieve the same result (or can we? 
) but the underlying design philosophy is quite clear, and feels pretty similar to the Modern one.
The cultural damage and disconnect comes, in my opinion, due to the decades of Trad design that followed the Classic era.
Incoherent design focusing on the impossible task of simulating all the diegetic minutiae of a boundless imagined reality… while also not providing much needed explanations on how to play, exactly, this one game in your hands.
Of course they stand in the way!
Of course they require someone (usually the GM) to “fix” them on the fly, to add their own design work to plug the holes the rulebook has.
THIS affected the people that, amidst the Trad culture, thought it would be cool to revive the Old School. When rules felt like they were not in the way.
This fostered the later trend towards minimalism, although it was never really part of Classic designs.
…
Fix the OSR and NSR cultural bias against “rules” and I see no obstacle in them crossing streams with Modern designs. They are already very similar (if not identical) things 