Setting '123456' as a password on any non-trivial system is not "the shortest route possible to maximize their productivity." It would be setting the password as "000000"
I'm not sure, I think it's a little more ergonomical to hit six different keys compared to hitting a single key precisely six times.
The guys who are really into keyboard layouts would argue vehemently that 123456 is more ergonomic as it's an "inward roll" vs 6 consecutive presses of a key that aligns to the pinky