Comparing the old Napoleonic armies with the current ones can be a bit off. Remember that arriving IN formation, and maintaining formation were more important in those days. You fought in those massed formations, and you had to keep them formed. Moving slower, but keeping formation would be more important than arriving at an attack positon at a certain time, and launching a coordinated attack as today's military's do it. So it's tough to really compare the two.
The old armies would be staying in those formations, and moving around the battlefield and fighting in those formations. Current militaries will move fast, then deploy. While the transition can be seamless today, it still occurs.
Considering the requirement to maintain a fighting formation, the 2.4 MPH figure arrived at is clipping along pretty good for those days.
Ross