People take notes for various reasons. I find that a lot students just simply jot down whatever is written on the board without considering if it is important, already know, obvious, etc.
However, there is also another reason to want to write everything down. When I used to teach intro physics, I explicitly tell the students to not only pay attention to the material being presented, but also pay attention to how I approach certain problems. I was trying to teach them not only the subject matter involved in solving a problem, for example, but also a good problem solving
technique. This last part is often neglected in many physics instructions. So in this case, it is pertinent that one tries to copy everything, even things that appear "trivial". Let me illustrate...
Let's say we are tackling an electrostatic problem involving an infinite line charge. A typical problem would ask for the E-field at some distance away from the axis of symmetry of that line charge. For most students, knowing where to start itself is a major task! So when I'm tackling this problem for the class, I would literally write on the board:
Since this problem is highly symmetric, we can use Gauss's Law to solve this problem
Now, for most "bright" students, which is absurdly obvious. But to an avarage or lagging students, this tells them clearly why we are starting off right away by choosing Gauss's Law and not Coulomb's law, the latter of which can involve painful integrations of several variables.
Next, once we know what to use, there is another "obvious" statement that is required:
In addition, the problem has a cylindrical symmetry, and so the problem should be solved in cylindrical coordinates and most appropriate geometry of the Gaussian surface that we should construct is a cylindrical surface.
Again, this may appear to be painfully obvious. But you see, writing it down explicitly accomplished two things: (i) it clearly stated the decisions being made based on the PHYSICS of the problem, and (ii) it allows one to remember WHY these choices were made weeks or months from now when one is either reviewing or studing it once more.
I wrote these "obvious" things down almost without fail each time I tackle a problem, and it may have bored many students who may have thought I'm simply wasting time. However, these are the intangible skills that the student must have in tackling such problems. Most physics instructors simply write down these things without the explicit explanation why such-and-such were used and why were they used THAT way. The ability and skill to do that IS the physics part of solving the problem. Once we have set those up, the rest is just mindless mathematics to grind away!
So yes, maybe in some instances, there is a need to write down all the painfully obvious details, especially if the instructor is also trying to instill a habit of good problem-solving technique. Such things may not be that crucial if one has already mastered that particular topic, but for most of us "average" people, we always have to put some effort into making sure we understand something. So sometime, writing everything down does help.
Zz.