Gearbox designers should avoid integer ratios like the plague.
For mechanical reasons.
Integer ratios will accelerate wear and tear because it increases the frequency with which tooth A on the driver gear will meet tooth B on the driven gear.
This frequency is known as the hunting tooth frequency, which I've explained in more detail here.
Regarding 1:1
1:1 is a special case known as direct-drive. The input shaft is locked with the output shaft, so the above argument doesn't really apply.
I believe Wikipedia sheds some reasonable light on this matter:
In an era when different models of car with different wheel sizes could be accommodated by simply changing the final drive ratio, it made sense for all transmissions to use direct drive as the highest gear. As noted earlier, however, this would cause the engine to operate at too high an RPM for efficient cruising. Although adding the cruising gear to the main gearbox was possible, it was generally simpler to add a separate two-gear overdrive system to the existing gearbox. This not only meant that it could be tuned for different vehicles, but had the additional advantage that it could be offered as an option, which was easy to add.
I interpret that to mean there are a few motivating factors at play (denoted in brackets):
1:1 isn't sufficient as a final gear ratio because the resultant engine RPM is too high for the cruising speeds of modern vehicles (mechanical)
It is simpler to design the gearbox to have two overdrive gears than have direct drive with one overdrive gear (cost, manufacturing, engineering)
A design with two overdrive gears is easier to tune for different vehicles, making the same gearbox design more universal (cost)
