Last year, when GPT-3 was already around, people managed to get it solve some of the earlier problems itself, but not the later problems. This makes sense, because the earlier problems are made deliberately easier, while more difficult problems are saved for later. To eliminate this "busy work" aspect would require knocking out those easier problems, which would be a loss for those who can't solve the later problems at all.

Even then, it seems like something being beatable by a computer doesn't make it pointless to do as an exercise. We still teach children to add and multiply, even though computers can do these things billions of times faster than a human can and have been able to do so for decades. We believe that being able to do these things in ones own head is valuable even if it isn't the fastest way of doing them. Besides, there are still many people who practice and enjoy chess even after computers beat humans at it, and in fact many people integrate computer chess programs into their practice and analysis of chess.

The advent of code problems are already "busy work", in the sense of not making much sense, and having numerous complexities thrown into them for the sake of it. People have still enjoyed them for the competitive aspect, or for the fun of solving a puzzle. Those aspects don't change when you introduce an AI that can solve them faster.