It's a simple question, and the answer should feel obvious by the time we get to it. But it's worth (ha-ha) taking a look at some ways in which it isn't worth it first.
A 'career' is presumably what you do to sustain yourself (and any dependents). That is, what you do to continue your existence and to ensure it is of a certain quality. Because we live in a commodified, capitalised society - one in which it is possible to buy almost anything with money - it will be simplest if we think of a career as an activity whose purpose is accumulating money.
Note: I said purpose. Not only value. Many careers have plenty of value beyond their core purpose (that's kind of the point here), but the fact remains that anything you do as a career is something you're doing to make money. Okay, except subsistence farming, but last I checked you can't grow novels.
That's what a career is, then. So what's a good career? We can divide the values a career might have into two categories, which we might (with a little stretching) call 'professional' and 'qualitative'. Professional values are things about the career as a career, such as its reliability and its efficiency (i.e. how much money you make per unit time spent working). Qualitative values are features of the activity done as a career, but which would persist if you did that activity as a hobby or on a non-professional basis.
So, for example, the professional values of being a teacher are things like the pay rate, holidays etc. Qualitative values would be the satisfaction of nurturing young minds. If you teach as a volunteer, you still get the qualitative values, but you don't get the pay packet.
Given my past blog posts about writing, you can probably guess where I'm going with this. The professional value of writing as a career is minimal, and this can be shown with some fairly simple maths.
Let's - as always - take the example of a debut author publishing a debut novel (it keeps the analysis clearer). In this case, we'll stick to traditional publishing because there's a stabler model there. It takes a huge amount of effort to sell a first novel to a publisher. You've got to write it, edit it like mad, query agents until you're blue in the face, edit again to satisfy the agent, and then if you're lucky it will sell. Then you edit all over again and again for the publisher and the book goes to stores (roughly).
Take a stab at how many hours' work are involved on the author's part in that process. We'll leave out promotion for now, because that's a much more variable expense of time and effort. I reckon I can churn out a first draft of a 60-70,000-word novel (short, by modern standards) in about 100 hours. Let's say twice that for editing and polishing.
How many queries do you need to make to sell a book? Say you get lucky, and it takes twenty-five. That will only happen if you've researched who to query and tailored your query to suit each time (and you get lucky). Is four hours per query out of the question? I don't think so, and it keeps the maths easier.
Another hundred hours for agent edits (if that sounds like a lot, remember it's not much more than an hour per thousand words). I don't know how much work an individual author would do in getting a publisher - my understanding is that should be left to the agent, but we can assume most authors will have some involvement. Still, we'll leave it out of the calcluations, and move on. Call it another hundred hours for publisher edits (again, optimistic).
Call it 600 hours, optimistically speaking. That's 75 8-hour working days, or fifteen working weeks. For which your pay is going to be an advance of, in all likelihood, something around the $5000 mark. If you're lucky, you'll earn that out and get some royalties as well. You might manage to turn your 600 hours of work (spread out across two to three years already) into a few thousand dollars across the first year or two of publication.
In all, you'll have made less than $10 an hour, unless you get very lucky. $10 an hour is (at time of writing) about £6.30. British minimum wage for over-21s is £6.08. At my part-time, entry-level support work job (a job with a lot of qualitative value, I should add), I make over £10 an hour. As far as professional value goes, writing is worth little more than flipping burgers, and has about as much job security.
(Sidebar: Yes, I'm going off the UK minimum wage. It's the one I know about. As I understand it the minimum wage in the US is a much more complicated issue, and politically loaded).
Anyway, I'm not going to deny that writing as a career is worth it (otherwise I'd stop, and go looking for some other job). My point is simply that the value of writing as a career is not the money. It's everything else - the intellectual stimulation, the satisfaction of completing your own projects, the interaction with readers, getting the voices in your head to shut up for a moment.
And that's never going to change. The things that make writing a crap career for professional value (particularly the job security issue, which we haven't even gotten into here) are never going to go away - they're structural features of the creative industries, even on digital-age business models like the new self-publishing.
One of the benefits I've found with giving so much work away for free is that it's made it much easier for me to focus on the qualitative values of my writing (and it's not like I don't have to worry about money in my life outside of writing - I'm scraping by on barely £5000 a year at the moment). So my advice is, whenever you're getting wound up about pricing, piracy, industry prejudice, business models or anything else, remember where the worth of writing really comes from.