The Birthday number is the simplest position in the chart: take the day of the month, reduce it, keep a master number if one appears. Because it needs only one figure it is the position most often given in popular writing, and the one a reader can compute without a chart.
Its simplicity hides a dependence the system never addresses. The day of the month is not a fact about a person; it is a reading taken from whichever calendar was in force. A birth recorded in the Julian calendar falls on a different day of the month from the same moment recorded in the Gregorian, and the gap between the two reached thirteen days in the twentieth century. Countries changed over at different dates, Russia only in 1918, so for a great many people the day on the document depends on which administration issued it.
Lunar and lunisolar calendars make the problem structural rather than historical. A birth recorded by the Hebrew, Islamic or Chinese calendar has a day of the month that does not correspond to the Gregorian one at all, and converting it is a choice about which record to treat as the real one.
Midnight adds a smaller version of the same difficulty. A birth an hour either side of it changes the day, and therefore the number, and the recorded time depends on the local convention and on whoever was holding the clock.
None of this makes the position unusable in the tradition. It does mean the figure records a document.