One downside of temporary workers that hasn't been mentioned yet is that they lack significant experience in any given project/task. Many projects/tasks are so complex that they require years to master, and months just to get into things. Thus, a temporary worker, no matter how brilliant or educated or experienced in the field in general, will not be a viable replacement for a steady worker. So, I don't see freelancers replacing long-term employees in the main industry any time soon. Which suggests that a demand for short-term workers will peak at some point.
Another factor is that many freelancers may soon realize that being a freelancer is a crappy arrangement. Yes, it provides flexibility and a relative freedom, but it lacks stability and the perks of a steady job, and often doesn't pay that well. This suggests that eventually freelancers and the kind will become increasingly discouraged from entering these arrangements, leaving the spot for those who can't find a long-term job, which will reduce the quality of the on-demand work, and in turn discourage the employers from using short-term workers.
Another bubble burst, so to speak, much like online coupons.
However, even if I'm right, I doubt that we will go back to the steady jobs of the 20th century. More likely, the job market will evolve to a new, as of yet unfathomable state.
As an entrepreneur, I like to believe that entrepreneurship will become the dominant employment arrangement, where you work on something for a long while without being paid, and then get paid a lot all at once. If a stable startup theory emerges, startups become more predictable, and the success rate improves drastically, then such an evolution would be all but inevitable.
Then again, it could be something else entirely. Perhaps the technology will advance to a stage that human labor will no longer be required and we will be free to pursue any activity we desire without worrying about living expenses as we know them. Or, perhaps we will become slaves to our AI overlords, working without any pay whatsoever until we die of exhaustion. Who knows.