I don't have a great understanding of the history of engineering, but I get the impression that working from the theory backwards can often be helpful. For example, Turing developed the basics of computer science before sufficiently general computers existed.

The first computer was designed by Babbage who was mostly interested in practical applications (although admitedly it was never built.) 100 years later Konrad Zuse developed the first working computer and was also for practical purposes. I'm not sure if he was even aware of Turing's work.

Not that Turing didn't contribute anything to the development of computers, but I'm not sure if it's a good example of theory preceding practice.

In AI in general this seems to be the case. Neural networks have been around forever, but they keep making progress every time computers get a bit faster. For the most part it's not like scientists have invented good algorithms and are waiting around for computers to get fast enough to run them. Rather the computers get a bit faster and then it drives a new wave of progress and lets researchers experiment with new stuff.

Anyway, AIXI has been used to develop more practical algorithms.

Forgive me if I'm mistaken, but is AIXI really that novel? From a theoreticians point of view maybe, but from the practical side of AI it's just a reformulation of reinforcement learning. MC AIXI is impressive because it works at all, not because there aren't any other algorithms that can learn to play pac man.