An autorouter is perfectly fine for whole classes of electronics. As a basic rule, if you'd happily assemble the circuit on a breadboard or with jumper cables and not worry about signal continuity, the autorouter will be fine.
It's only when you get to higher speed or higher currents that an autorouter won't have the context needed to effectively route the circuit.
I think I should have added the caveat "with the typical information we give it".
I suspect that if we made enough effort at the schematic stage to properly annotate all the nets and define the types of signals flowing around the board, an autorouter could do a superior job to a human (from an RF emissions and trace current sense).
I've never seen a schematic with that level of annotation though. So as long as the person doing the layout has to use external knowledge of what they're laying out, autorouters will struggle.
In theory you could make EDA software which incorporated a full circuit simulation which was then fed into the autorouter to provide a layout optimised for low-EMI and high efficiency. That would be nice!
It's only when you get to higher speed or higher currents that an autorouter won't have the context needed to effectively route the circuit.