This seemed to be what a PhD was all about, but it's not what I've experienced. I've just completed the first year of grad school, and while the classes have been interesting, the expectation is that you already have an advisor when you arrive (or at the latest at the end of your first year) and you hit the ground running pumping out papers. There seems to be little opportunity to explore computer science as a whole or to work towards one singular result. I recently had the pleasure of chatting with Peter Sarnak about CS graduate education. He said that CS is in a weird spot between traditional engineering disciplines and the liberal arts, and that the need for grant funding causes departments to encourage students to work on whatever projects the professors are leading. But even he seemed a little surprised when I told him that our department's general exam is basically a presentation on the research you've accomplished so far.
I think this is unfortunate. First, because it goes against what I wanted out of a PhD. But also because it makes the PhD not much different than working in industry. If in either case I have to write code for some boss and satisfy my curiosities on the nights and weekends, why would I choose to do it for much less money and worse career prospects? I imagine this is causing the best and brightest to avoid academia in computer science, which seems bad for research and technological progress in general.