Well, we already elaborated about sub domains pro and cons, like here
The idea SEO wise is that a sub domain is almost like another domain of yours where you can exactly choose the keywords, unlike with domains.
So this can be interesting, this is for sure. The links you'll be able to exchange among sub domains can help out too, but I'm pretty sure Search Engine are not giving as much weight to these as they would with real external links.
On the other hand, since you can make accurate choices among all sub domains, you'll be able to build up a real good linking strategy. With both home and deep links, coming from the most related location of each.
And, if you manage to be well ranked is SERPS, you can end up with things like : http://www.google.fr/search?q=phpbb+seo&hl=fr
This is the result in the french world, it's a bit longer to compete with the world, but as you can see, phpBB SEO is not only first on this query, it's trusting 8 results over ten in the first page
We're still there in the English speaking world : http://www.google.com/search?q=phpbb+seo&hl=en
Then, another thing to take into account while you think about sub domains, is how will each one be active, with it's own topics covered.
In your case it looks like all the 16 websites are already true websites, with content updated on a regular basis and so on.
But it's an important matter, the main domain must, IMHO, be really active and have decent amount of content compared to it's sub domains.
You really don't want it to be treated as a link farm ( a web site almost only linking externally with few pages in comparison to the sub domains ).
That's the reason why we brought both phpBB SEO forum back under the main domain here. Have you read this
So here for the things to think about while you'll be making your mind.
Now, to really decide, it depends. The reasons why you are wondering about doing this are pretty obvious, but it's harder to tell if it would be of any good.
It really depends on your project and the way you'll manage it.
16 website is not few, and you don't want to jeopardize all the hard work already put into these.
These 16 domains must already have had results in SERPS, and be PageRanked. Now off course HTTP redirecting them would save most of it, but it would be harder to go back to the initial situation SEO wise.
All this depends on the 16 websites you have.
It could be interesting as well to start a new site kind of like you wanted, but keeping the magazines where they are now. This new domain could be the business interface to the magazines, like, "we are editing these magazines".
An occasion to perhaps talk about these in a different manner, finding common points and dealing from there with marketing and new collaborations, and to offer a more focused picture of your activities all at once.
This would allow you to give more backlinks to the actual websites, and to start a new one.
Of course, these are only hypothesis, my goal here is to give you some keys to think about all this.
What is for sure is that you'd better think about it twice before you move, and whatever you decide, to do it when you are ready.
Further analysis would require more data.