I'd like to see something which supplies a small daily dose of established science, but you'd probably need a writer who's as engaging as Asimov-- and even then, not that many people are interested.
The writing at Wikipedia tends not to be engaging. Admittedly, I'm generalizing from one example.
I'm not sure that this is a full-time job for just one person. If nothing else, getting advertising is work.
I think the Philadelphia Weekly is a pretty good free paper, but I read most of the articles and ignore the advertising.
I don't think the basic idea is bad, but I'd start with a website-- lower investment, more flexibility, and better feedback about what people read. It would be a better way to find out what actually engages people.
The problem with website is: how do you make people look at it? Especially those not already interested in topics you want to write about. The competition is huge.
(With free newspaper, the answer is: reading the paper you already have in your hand is easier than reading any other paper.)
If it's worth saying, but not worth its own post, even in Discussion, it goes here.