There's a certain line of thought in accelerator/beam physics connected to the question of the local/global dichotomy. I'll just put some preliminary thoughts, which is basically what I always do here anyway.
Let me start by linking to the book by Forest. In this book he continually makes the point that one should replace local Hamiltonian dynamics by global map-based methods in the modeling and analysis of storage ring physics. Of course one still needs to use some kind of local theory (a symplectic integrator) to get the global results to begin with, but the emphasis is on this separation of duties. He rails against the old school that mucks around theoretically in the local s-dependant Hamiltonian, basically saying that they never get very far because the real machines are so complicated as to make the approach useless.
Why has this new approach not completely caught on? Is it entirely due to idiosyncrasies and historical development of the field? Is it the old timers holding on to their beta functions and simple coupled theories and not allowing a more general approach that renders their knowledge obsolete?
This may be part of it, but I think there is also something fundamentally flawed about the approach from a scientific community perspective. Certainly there are local quantities and global quantities and global analysis of results coming from local quantities is quite important. The problem is that the physics model is never complete. There are always more local effects to include and if one takes a particular piece of physics and pushes this local/global picture too far, one ends up with software, methods and sociology that shows too much of a disparity between large and small.
The connection I would draw is to large corporations -- say Starbucks or Borders. On the one hand, these companies can accomplish certain large things quite efficiently. But on the other, they are going to change slowly in response to local requirements because they are defined in terms of their final goals. The analogy here is to the computer code that implements the model. (Part of my motivation for thinking and writing about this is my own frustration, partly just from lack of programming skills, in modifying a code based on these principles to do what I want. The structure is fine, but the scale is off for certain types of changes-- too much effort to do something small-- though some would argue that these things are useless, it is exactly here where the disagreement could be fleshed out.)
The problem with the local/global split is that it encourages this building of large structures without allowing many people to understand the workings at intermediate levels. It turns people into either workers or consumers, and leaves the power to mould the system in the hands of just a few.
I don't want to minimize the value of the particular local/global split that Forest advocates for storage ring physics. I think it is quite valuable and the clarity it provides is important. However from a pedagogical and sociological perspective, this leaving out of all forms of intermediate levels of understanding or analysis ultimately may prevent alternative more powerful synthesis and understanding to emerge, in addition to contributing to a polarized environment (though certainly no one person is to blame for this).