I'm with the OP on this. It's too easy to get distracted by all the awesome things you can do and learn when at Grad School.
> (a) become a broadly smart individual
Do you need to be in grad school to achieve this? Why not just read widely and do the odd course here and there? I also suffered from the 'learn everything' bug and I think it cost me. I'm confident in my ability to learn so a lack of knowledge in one area doesn't bother me.
> (b) do research later on anything else besides the tiny topic of your dissertation
This isn't true at all. Learning the skills involved in focusing on one area can then be applied to another area later on. I've moved between Physics and Neuroscience and was (reasonably) focused on each at the time. However, the grad students who succeed in academia tend to focus on one thing for many years, right the way through post-docs. It's only when they become tenured that they begin branching out more.
Yeah, it is, and it's a great way to add years onto a career move that is paying you subsistence wages.
You can attend other classes once you're a post-doc (unlucky) or a professor (better). Then, the university is paying you to be there, rather than someone else trying to find a salary for you in their limited grant funding.