I remember the 'half-step' gearing arrangement being more popular with touring cyclists than with racers. The idea was that with 5 (or sometimes 6) cogs in the back the difference between consecutive cogs was typically about 18% (a very popular touring/casual freewheel was 14, 17, 20, 24, 28) and this was a pretty big jump between gears. By using chainrings that differed by about 9% you could cut the size of this jump in half.
For example, my touring bike has 'half-step plus granny' gearing with chainrings of 50, 46, and 30. The 30 tooth is pretty much reserved for substantial hills/mountains and the other two are used for most riding. So when riding in the 50 & 20 combination and wanting to shift up to a higher gear I can either jump all the way up to 50 & 17 (an increase of 17.6%) or I can shift in both front and back to the 46 & 17 combination for an increase of only 9.2%. Check out all the combinations and you'll see that this half-step arrangement gives pretty even spacing of gears at 9% intervals, but at the expense of needing to do lots of double-shifting with both derailleurs. Touring cyclists facing long stretches of riding between shifts could afford the extra time to do the double-shift when needed in exchange for getting just the right gear for the conditions.
Most racers of that period preferred the alternative arrangement (sometimes called 'alpine') with closely spaced cogs in the back (say 13, 14, 15, 16, 17, 18 for a 6-speed) and something like 54/42 in the front. Almost all shifting is then done using only the rear derailleur and the front is used to choose the rough range: the 54 for flat or downhill stretches, and the 42 for climbs. Made for quicker shifting to respond quickly to attacks by competitors.
The move to 10 cogs in the back has essentially eliminated the rationale for half-step gearing which is why it isn't found on current bike models.