Too broad or not too broad…
I would say "it depends", because we've all seen two kinds of "career questions":
the on-point questions, not being sure about some detail on their career path.
Example: "I'm currently studying maths while targetting a cryptanalyst job. Could adding statistics courses to my schedule be beneficial for my later career?"
the broad questions, not being sure about anything.
Example: "I want to work in the crypto industry, what do I need and where should I start?"
While I don't really regard career questions to be generally off-topic, I do have to say that most career question really give me a hard time by simply being too broad.
Good versus bad advice…
Besides that, those "career questions" always tend to be a bit like the "legal questions" we get. They're hard to answer in a few lines, and for most of them there will be no "one correct answer". I guess the reason for that is that the success of career decisions will depend on many things: education, experience, talent, luck, timing, etc. So, even while I do try to provide usable feedback most of the time, it always tends to give me a bit of an uncomfortable feeling because what might well be good career advice for one person, may well be bad career advice for another.
Also, I've frequently catched myself wondering if it is possible to answer specific career questions, while completely blending out personal opinion. Unless the career question asks about standard career paths that are widely accepted in the related industry, it's hard not to fall back on personal experience/opinion.
It all really depends on the individual question asked and how it's asked. So, I will (until further notice) continue to regard "career questions" to be on-topic, as long as they don't fail the usual rules… by being too broad, by asking for personal opinions where no definite answer is possible, by being "shopping-list" questions (like asking for "the best" university), etc.
But if it were my personal choice: I would prefer to rule them off-topic as I doubt we'ld be losing much. Fact is, good career questions are rare (especially at Crypto.SE) and @D.W. has a point with the FAQ.