One: So was David, Solomon, all of the kings, all the men of the other 11 tribes, most of the prophets, all of the Twelve, anyone over fifty or under 25, anyone with a handicap, any foreigner (such as Job)...I am not sure exclusion from the priesthood meant much in terms of value...
Two:There WAS a "lay" position that normal men and women could aspire to--the Nazarite role. This was a vow-based position of holiness in Israel. It was open to women and men, and had the same level of ritual purification requirements as that of the HIGH PRIEST! It actually involved some of the rituals of the Levitical priesthood (e.g. sacrifices), but did not require lifelong tenure. It was open to men and women, and could be done any number of times in life.
Theologically speaking, every Israelite WAS supposed to be a 'priest'--to the rest of the world. In Exodus 19.5, we read: Now if you obey me fully and keep my covenant, then out of all nations you will be my treasured possession. Although the whole earth is mine,
6 you will be for me a kingdom of priests and a holy nation.'.
From an overall standpoint, this 'exclusion' was not that big of a deal...any value that MIGHT be associated (inappropriately) with it in the culture (in terms of "special relationship to YHWH") was available to ANYONE who would consecrate themselves to the Nazarite commitment.