To point one: a cheap way to get off the ground. The idea that there is some demand is not really the question. The question is, is there enough to be a successful enough venture for the owners. Antenna and Me are very low cost ways to get some use out of broadcast sub channels, and the jury will remain out as to the long term viability of the business model.
It's also worth pointing out that RTN is so "popular," it has already been through one bankruptcy. And a lot of the local stations that air these networks actually pre-empt them with impunity when they can sell infomercials in their place. As you say, it's just filler to the broadcasters.
As far as the purpose of cable channels changing over time, keep in mind that when Nick at Nite started, it was literally the only place where you could watch most "classic" programs. Now you can see them on DVD or Netflix or Hulu any time you want. And if you're mostly interested in just seeing the most famous moments and episodes from a series (which is how most people watch classic TV anyway), then you can probably find what you're looking for on YouTube.
GSN was born concurrent with digital cable, at a time when cable providers suddenly found themselves with the ability to offer hundreds of channels, but without the actual content to fill them. At that time, the channels were in a startup phase when ratings were almost beside the point. That's no longer the case, especially for channels like GSN that aren't owned by companies that also have more popular channels that they can sell as a package. That's part of how TCM gets so much carriage: Turner can say if you want relatively popular channels like TNT and TBS, you've gotta take TCM, too. The most signifcant channels that Sony owns are a couple of small sports channels and Audience Network, which is basically a loss leader that DirecTV uses to try to get more subscribers.