For some things, this is basically the case---if I'm doing software development work for a company, I'm paid hourly. I might not be on the company healthcare plan, but I get paid for all the work I do, and generally, it's a lot higher hourly than a staff employee. I still get the benefit of setting all my own hours, choosing my clients, and essentially running myself as my own business. It's quite nice.

However, that isn't really different from freelancing, is it? You still don't get benefits. Really, it's about the unit of work; with software dev, it's about the hours I put in. With freelance writing, it's about the individual articles I submit. I'm simply paid per article in that case (though other employers may charge differently depending on the content type, not sure).

Part-time generally is a designation for employees earning a wage and working at a physical location. Like a Starbucks employee. For an online publication, it's simply much easier to manage one set of staff writers, and many freelancers, rather than trying to track everyone's hours (which you can't accurately do in this setting anyway).

Worth noting that you do have to pay an extra 7.65% FICA tax yourself in the case of contracting work, since you are employer and employee. This is usually accounted for (or at least understood) when you set or accept your prices. Usually, for waged employees, this simply leads to lower hourly wages in most cases, provided you aren't making minimum wage.