Some of these guys "eat engineers for breakfast" but they still can't "wake up, ... be presented with a new problem no one else has addressed before, and build a machine to solve it, all before dinner." The timescale for solving novel problems just seems to be a lot longer. Even building a steam engine from a kit is a matter of weeks on a manual machine.
If you need a key copied, a lock pick ground from a street sweeper bristle, a transfer punch made from drill rod, or a weird left-hand screw with a strange thread pitch, they can probably do that before dinner, yeah. But that's because those are well-understood and fairly simple problems.
CNC machining opens up more possibilities, but the timescale is still longer. You don't want to find out your G-code is buggy by crashing a US$150k milling machine; crashing a mill is more like crashing a truck than crashing a computer. So machinists are generally methodical, patient, and careful.
