I'm reasonably sure the long holding time is there for two reasons - one is that mincemeat was originally a preserved dish, with the alcohol and spices and fats used to preserve the meat (when it was included) and fruit in the dish. So recipes may mention how long the pies can be reasonably held, for preservation or for the convenience of cooking early or making a large batch once instead of several smaller. The other reason, perhaps more recent, is that the flavors change over time, as the alcohol seeps in and the flavors meld and marry in the mincemeat (think pickles or alcohol preserves, it takes time for the flavors to change). The time the recipe mentions for maturing might be the time over which the flavors are still improving as they are stored, or the compromise time between when it reaches a state the recipe-makers find most pleasing, and when the recipe-users find convenient (that is,it might not improve if matured longer, it might get worse, it might keep improving but most people get impatient).
In neither case should eating the mincemeat early be unsafe. Maturing it significantly longer than the recipe allows for might be less safe, since the preservative qualities will depend on proportions of alcohol and spices, storage conditions, and other things the recipe depends on to make that calculation in the first place. And eating it early might give a less than ideal flavor, if the flavors haven't melded or mellowed or changed over time to reach the state the recipe makers intended.
So if you like the mincemeat as it is, and if you're impatient, there is no harm in eating it early; while if you thought the flavors were less than you hoped, perhaps harsh or dissonant, or you just have the extra time and patience, you may find the extra couple weeks of waiting worthwhile.