My guess is that it started as an administrative issue, i.e. the tax disk displayed month and year and so it wasn't possible to charge for part of the month, and having each tax disk end on a different date of the month would make it very difficult for the police to see with a quick glance if the car was taxed or not.
It's not really an issue any more in this day and age, police ANPR can check automatically if a car is taxed just like it checks if the car is insured and has a valid MOT. But I guess that, like the QWERY keyboard, it stuck... (that, and the fact that the DVLA will be losing income if they changed the system now).