The smaller front wheel allows a shorter head tube and therefore a a lower standover height (ie. smaller frame). It allowed manufacturers to use standard lugs rather than develop special lugs for odd angles. Of course, this was prior to the widespread adoption of TIG welding, which eliminates lugs and would have allowed a sloping top tube frame. Using the same size wheel on the rear has the advantage of only having to carry a single size of spare tube and tire but means the manufacturer has to spec standard gearing to achieve the desired gear ratios.
Also, many smaller adults have a stigma about riding a bicycle with two, smaller than standard wheels. They perceive it as being a child's bicycle and not an adult model. At least with one standard wheel, it is clearly an adult bicycle designed for a shorter person.
At the time, the concept was a popular solution for very short riders and was used by numerous manufacturers. However, very short riders are usually female and they make up a relatively small proportion of the cycling public, so most manufactuers only offered one model in these very small sizes and they were generally not a top end model. The concept also got quickly replaced by 650C wheels (which are bigger than 24" but smaller than 700C) and TIG welded frames with sloping top tubes. Consequently, you do not see them too often.
This particular model was offered in 1987 is a mid-range grand touring bicycle. For curious readers, the frame size is 46 cm (CTT). Miyata was arguably the best of the Japanese mass volume manufacturers. Their bicycles are consistently well designed and built, and they ofer excellent value at their respective price points. Provided it has not been abused or worn out, and it fits her well, your girlfried should be very happy with it.