I somehow agree that this is not entirely a design problem, but a production one... BUT...
Designing is knowing some production process, and in my opinion, this is important to optimize costs, which it is also a part of the design.
folds tend to tear more
This is not an issue for me. If I want something to be everlasting I would recommend synthetic paper.
covers warped because they were printed in the wrong direction
It could be the case with some types of thick paper, or some types of plastified surfaces, humidity or some other issues. But, yeap, some cases could be prevented somehow considering the fibers of the paper. But probably it is simply a poor material choice. I will address this later.
Note this. I am not sure if this a language issue (My native language is Spanish). But I do not care about grain... I care about fibers.
The difference, in my opinion, is that grain refers to the texture of the paper. A rough paper for watercolor painting has grain. But the fibers of a coated paper could not be easily spotted by touch.
So, regarding fibers I would separate several things:
Paper, thick paper or cardboard. I also have a limitation on the language here.
By cardboard, I am referring to SBS for example, not any type of corrugated cardboard. A thick paper could also, be for example more than 300g. In the explanations, I would only refer to it as paper.
Type of printing machine.
Let's see how a print fiber should be on a paper
A. An offset sheeted printer does not keep the paper totally flat like a flatbed printer.
B. It needs to manipulate a bit the paper.
C. So, the fibers need to be perpendicular to the printing direction.
Let us assume we need a smaller piece of paper because our project is small in size.
D. Why we just do not cut the paper and insert it in this same direction? Because inserting this paper, with the smaller side to the machine can cause the tail of the paper to move, which is a more important matter to consider than the fiber.
E. So we need to insert the paper rotated, with the fibers parallel to the print direction.
F. This can make the paper stiffer, so it does not bend when the machine needs it to bend.
Sometimes, depending on the 3 different variables we have, this direction of the fibers could be a real issue or not at all. Mainly the size of the paper and the thickness.
In a "practical" user based way, it is more friendly if the different papers bend nicely on a magazine (G).
Using a wrong fiber direction can make some sheets feel awkward and stiff. (H)
But regarding covers warping... yes, it could due to wrong fiber direction (I)
but the cases (J) and (K) have the proper fiber direction and the warping would still be an issue. This is due to poor management of the materials more than the fiber direction.
The last issue is regarding folding. On a tri-fold brochure you normally want the fibers to be parallel to the fold. But it is more important to avoid breaking the coating of the paper, handling the paper folding with the right speed on the folding machine.