...until the computers shut down because of a simple power outage or an DDoS attack. Then the Luddists and their looms will definitely win. When you rely on technology, you rely on a single point of failure.

There's also the question of speed/efficiency as well. Memorizing a fact and utilizing muscle memory can be much quicker than Googling for Stack Overflow answers every day ("memory caching"). And the faster you solve one problem, the faster you can move onto the next problem.