Great Question
I'm in a similar situation to yourself, in that I can hit the ground running in basically any aspect of IT, and every job available seems to be for only one skill.
I think there is something really interesting happening at the moment in IT.
If you go back even a decade, a typical web development company would have say a team of dedicated HTML/CSS developers, a team of dedicated Javascript developers, a dedicated team writing the server side code, and an IT department who looked after the servers/network etc.
Recently there have been all sorts of really cool frameworks released which quite simply make everything easier. Where it would previously have taken a team of HTML/CSS developers to make a nice looking website, this can now be done as part of one persons job with Twitter Bootstrap. Same goes for the Javascript using something like jQuery/Angular, and the server side code with a framework like Ruby on Rails or ASP.Net MVC.
As for the server stuff, if you are using a cloud service like AWS or Azure, you really don't need a team of people to maintain all of that, again it can now be done as part of one persons job (that person being the IT generalist).
I think there are a lot of companies out there that still have that old structure, but are using the new frameworks + the cloud. They have a lot of employees who have been there for years, and they can't just fire them so they try to find a role for everyone. When you apply for a job there, they try to fit you into that structure also, in a way that others don't feel as though their jobs are threatened.
Because you are only hired to only do one thing, you only get paid for one thing. The solution seems to be startups, who welcome the fact that you can wear many hats, but then startups don't tend to have the cash flow of a larger company, so you may make more or less the same as you would in a larger company doing one job, but at least the work will be more interesting. I would definitely choose this over a single skilled job at a larger company, mainly to keep my skills sharp and up to date in all areas.
I don't really have any answers, just thought I would spill my thoughts on the situation into a textbox and see what others say.