I've been thinking a bit about my own lack of specialization lately...and, its negative impact on my value to a larger organization than my own company.
I suspect I'd have a hard time finding employment doing the kind of work I'd want to do at the kind of salary I'd expect to earn. I'm a decent programmer with broad but rarely deep experience, a better than average sysadmin with ridiculously broad experience, a passable designer (better than half of the "real", but merely average, designers I've worked with over the years, but so far behind the good ones that I'm hesitant to use the same term to describe what I do when I build websites), a passable sales person, a pretty good writer and copy editor, and the list goes on and on, because I've run my own companies for the past 17 years. I've touched everything that a business has to do, and I've somehow muddled through and kept the bills paid and the customers coming back.
But, I'm not a "rock star" at any particular task. I couldn't wow anyone with my algorithms knowledge, though I've always figured out how to solve the problems I needed to solve. That's not a very compelling sales pitch when talking about a $100k+/year job for a company that has a specialist in all of the above-mentioned roles.
So, I think it really depends on what you want out of life. If you want to maximize security and income, focus on a high value skill. Become the best in your market, or as close to it as you can manage. Eschew all distractions from that skill; don't fuck around with weird Linux distros, figuring out how DNSSEC works, building your own mail server, setting up CI, self-hosting all of your own services and web apps, or otherwise becoming a "jack of all trades, master of none". If, on the other hand, all of those distractions sound like the best reason to be in tech (and, that's the way it's always added up for me, even when it's cost me time and money), and you're willing to take on a lot more risk building your own business (whether consulting or building products), I guess being a jack of all trades isn't so bad.
But, and this is a big but: There's only so many hours in the day, and so many productive days in your life (and you also have to take time away from productivity to have a life outside of work/tech). As I get older I realize more and more that I have probably valued my time less than I should and valued my ability to effectively DIY my way to success too highly. I've spent many hours fucking around with stuff that I could have paid someone a few (or a few hundred, or a few thousand) bucks to make the problem go away, and it would have been worth it in a lot of those cases.