I don’t think programmers will be obsolete; but I think the skill set will shift away from the analytical and mathematical traits that set programmers apart today, towards the fuzzier knowledge of the humanities. (Though my personal belief is that liberal arts educations must include science and mathematics as a core pillar.)
Specialization in algorithmic and mathematical thinking will still be of extremely high value, but the level of achievement required to be successful in that area will likely be crushingly competitive.
But, this is just a fun guess — let’s check back in ten years so we can see how utterly off base I was :)
People thought the same thing in the 80s....
Also, given that computers can test stuff on billions of people, I would say there is a good chance that you could have popular pieces of music and art that are produced largely by algorithms in the very near future.
But then you have to be clear-eyed about what we're talking about here: from the perspective of a college student, is it worth paying 1-200k[1] to become more worldly, with some auxiliary benefits to their income potential? I would probably still send my (future) kids to such a place, but then I'm in a pretty high income/wealth percentile. I suspect that many people (including my family when I was a kid), looking at this clear-headedly, would rationally decline this deal. If you think the pricing of college reflects the "broaden your horizons" aspect instead of the perception that it's "protection money for a middle-class career", you're sorely mistaken. Which means there are and can be far, far, far more cost-effective ways to broaden your horizons, particularly in the era of Internet communities, cheap travel, and all of humanity's knowledge at your fingertips at all times.
[1] I'm aware that there are ways to get through college more cheaply, like starting in community College. But a system in which the majority of people are going through ccs first is a very different system, so the thrust of GP's point still stands.