The priesthood in our time

Hello Rabbi
According to tradition, there were 600,000 men at Mount Sinai, and a total of probably between 2 and 3 million Jews.
Of these, only a few were priests – Aaron, his sons, and his grandchildren who were born until then.
That is, the starting condition is a zero percentage of priests out of the total population of the people of Israel.
Additionally, statistically speaking, there is no reason for the percentage of priests among the entire Jewish people to increase, since this is a lineage that only passes through one side (father) and not through both sides. Various hypotheses can be put forward for the increase in the number of priests (exceptional economic status, certain exemption from wars, special Torah status that may reduce the scope of assimilation), but they are not particularly well-founded and counterarguments can be raised against them (priests may be disqualified, conversion is only to Israel – so the denominator increases and the numerator decreases).
Does the rabbi have any comment on this question in light of the very high percentage of priests in the Jewish people today?
(There are of course additional historical considerations such as the disappearance of the ten tribes [therefore the percentage of priests increased] and in the Book of Ezra it appears that the percentage of priests in the Return to Zion was particularly high, but this does not really account for the clearly unreasonable numerical gap.)