Question

Hello Rabbi,
According to tradition, at the Revelation at Mount Sinai there were 600,000 men, and in total probably between 2 and 3 million Jews.
Among them there were only a few priests—Aaron, his sons, and his grandsons who had been born by then.
In other words, the initial condition is an almost negligible percentage of priests out of the general public of the Jewish people.
In addition, statistically there is no reason for the percentage of priests among the Jewish people as a whole to grow, since this lineage is passed only through one side (the father) and not through both sides. One can suggest various possibilities for growth in the number of priests (an unusual economic status, some exemption from wars, a special Torah status that might reduce the extent of assimilation), but these are not especially well founded, and against them one can raise counterarguments (priests can become disqualified, conversion adds only to Israelites—so the denominator grows and the numerator shrinks).
Does the Rabbi have any thoughts on this question in light of the very high percentage of priests among the Jewish people today?
(There are of course other historical considerations, such as the disappearance of the Ten Tribes [so the percentage of priests rises], and in the Book of Ezra it appears that the percentage of priests among those who returned to Zion was especially high, but that does not really resolve the plainly unreasonable numerical gap.)