When I first read this, something about it bothered me, but it took me a little while to pin down what it was.
It's that it's overly prescriptive. You've heard the old thing that some people are visual learners, and some audible learners, etc? It's a a cliche, but there's some truth there. For some people, sketching something out on a board is the best way to work through a difficult problem. For others, writing down the problem is far more effective. For others still, the best way is to talk through the problem with somebody else. And for some, the most effective way is to sit back, close their eyes, and think on it.
It's a very personal thing, and depends on how your brain works. The problem is not that thinking is a universally bad approach, but that it's what a lot of people default to even when it's not the optimal approach for them. The real reason for this, I think, is that it's the one approach to working through a difficult problem which doesn't require any special tools or external action. You just have to stop what you're doing and focus. No need to pull up a whiteboard, or write an e-mail, or find somebody to talk to. This makes it an easy default.
So it's a problem that people who don't solve problems effectively that way still try to do it, but I think it's very important to acknowledge that some people DO effectively solve problems that way.
For what it's worth, methods that work for me, in order of effectiveness, are: writing about them, talking them over with other people, and then thinking and drawing. Yes, I put drawing (your recommended approach) on about the same level as just thinking. I know drawing is very effective for others, though.