It's a good question and I keep tripping over.
I am a director writing my first original screenplay and I constantly go back and forth between including angles and not. One day I will put them in and the next day I will go back and remove them all.
It's a tricky one. On one hand I want to show the way I visualise the drama unfolding photographically but on the other hand I don't want to bog down the reader with technical detail when they should be deep in story.
As a first time screenwriter with the clear aim to direct what I am writing, I want industry people to see my flare for the way I will direct it as they read... but there is a big danger of over doing things.
PT Anderson is an obvious example but also a good one for a guy who is probably an equal talent at writing and directing. Take a look at Boogie Nights, it has camera angles thorough it and it reads similarly to how it was directed and cut. So I think the script worked as a clear blueprint for the picture he wanted to make. When you read the script I think the visual style, tone and rhythm of the picture are clear but aesthetic ideas don't overpower the story.
Then take a look at Magnolia which is pretty extreme. At that time New Line said they would give him final cut on whatever he wanted to do next and his dad had passed so he went balls out and wrote an epic script with an abyss of detail. Read the first 10 pages, sooooo much camera direction. I saw the film before I read the script but my feeling is unless you are someone who reads a LOT of scripts it could distract you away from the story.
Perhaps if you read Magnolia without camera direction and PT just said "it will have the intensity of Goodfellas in the way I direct it, that could have been enough to understand how it played out in his head. BUT the benefit for him at the time of writing was (because he knew what ever he wrote he'd direct) he could just create the blue print of exactly what he planned on doing. He's also said in early interviews that he does 90% of the work in the writing and then he doesnt have to worry too much about working it out later. Or something along those lines. To be clear I love both films, just a hand example in regard to writing.
On the other hand have a read of Pulp Fiction. An incredibly visual picture with almost no camera direction in the screenplay. It's more or less a talking picture so it's the right approach. BUT QT knew he's be directing and he'd work out the detail in pre-production, it's worth mentioning he spends a lot of time on that kind of detail leading up to shooting. He's the opposite of Woody Allen.
Butch Cassidy and The Sundance Kid strikes a bit of a balance where by you know what you are looking at through the writing without William Goldman ever saying "camera" or "angle".
Jeff Nichols did a great talk about it that can be found on the On Story podcast. You can find it via iTunes. His school of thought is more in the William Goldman zone whereby you speak visually though action and description and let that tell the reader where you see the camera without resorting to technical jargon.
Perhaps it is about finding the balance and doing what is right for the story you are writing? I find the best scripts are the ones I read straight through without tripping over superfluous detail.
Anyway, they are thoughts. I better get back to adding and removing camera details. Later. x