Um... Okay, I'm not the children's book specialist. Just so we're clear, I rarely have represented children's books (a few times, like Rene Riva, I couldn't say no). So I'm not the expert. However, I've certainly been around children's books and children's book authors and editors. And in my experience, I would disagree with what you read. In my experience, most of the children's publishers want proposals to come through agents. (We can get into why that is, if you want -- a good agent knows what the publisher is looking for, helps the author make sure it's ready, know how to help prepare the proposal so it fits the publisher's format, understands the economics of children's publishing, etc.) So I'd tend to disagree with whoever wrote that article.
This is a good place for me to point out that, over the years, I haven't exactly been the "agent evangelist." I made a good living as a writer without having an agent. (Truth? I kept talking to them, and I always seemed to know more about the industry than they did.) Is it possible to make it in this business without an agent? Sure it is. But it's getting harder. Most publishers simply won't accept un-agented proposals any more. They've done that as a means of trying to professionalize the relationship. They've also done it because the scads of young editorial assistants they used to have don't exist any more, so they don't have the personnel to wade through the unsolicited slushpile. It doesn't get talked about much, but the fact is publishers now rely on agents to be the first filter -- to go through the material and clear out the dross. They expect agents to help bring in publishable, salable manuscripts that fit the house and are well-written.
Now, having said that, the role of literary agents is definitely changing. Self-publishing is exploding, publishers are moving toward more e-books, and no one is quite sure what this business is going to look like in ten or twenty years. To which I say... "yeah? and this is new?" Hey, publishing is a dynamic industry. We've never really known what direction it was headed in. We all get surprised by mega-sellers that come out of nowhere and take us in new directions (Left Behind, Twilight, The Da Vinci Code, The Shack). So I expect the industry will be very different in a few years.
That said, my guess is we'll still have publishers. People will still want information and entertainment. They may read it on a device, but somebody will still have to write it, and others will still edit and produce it. Authors will still need help with careers, and will still be looking for guidance on things like ideas and topics and writing. They will still need someone who understands contracts to handle the business side, and they'll still want someone else negotiating for them and singing their praises and protecting them. (As I've noted before, your publisher has a team of lawyers and accountants working for them. Who do you have as an author?) So I think those of us who are good at this job will continue to work and make a living. A longer answer than you might have anticipated, but those are my thoughts.