Here's an important question:
Do Presbyterians, historically, have clergy? Are their ministers clergy, and their elders laity?
And, as a follow up question, is such a distinction biblically defensible? Obviously, if we have clergy, and want to defend having such in a way consistent with our professed belief (that everything related to the church's worship and government is strictly regulated), then this has to have been attempted in the past. There's your research project.
Ch.Hodge argued: the effort to combine the elders with the ministers of the church in a single office, though maintaining the difference in "function" according to class might damp down the tendency, such a move would have one of two natural effects.
1) It would either laicize the clergy, leading to congregationalism. Or 2), it would lead to a new and hard division between the rulers and the ruled; it would lead to a pronounced clericalism, no less an issue than that found in the hierarchical denominations.
The genius of Presbyterianism cannot be sustained unless there is a robust, and lay-eldership. As an analogous illustration, consider how the genius of the constitutional republic has devolved into rule by elites, under the guise of a democracy; the original design of which was expressly erected to oppose both tendencies. Unless citizens are in charge of the House, they are no longer self-governing in a meaningful sense. Lay-representation in government is the design of Presbyterianism, and that idea was at one time appropriated and reconfigured for secular purposes.
If elders are laymen then they are not clergy. Clergy are ministers of Christ's government, the function of which is in a proper sense (not in a sacerdotal sense) to represent Christ unto the people--to be his mouth in the proclamation of His word; and his hands in the administration of baptism and his Supper. If the elders are summoned to the same work, without any distinction in what they do and why--not just for the sake of additional education, or "full time employment"--then who represents the governed in the assembly?
If the halls of power are captured by the interests of those in those halls, if they ALL see themselves as representing top-down authority, the government's interests, its secrecy, its finances, the rules it makes for the people to follow and who are not held to a common standard, who is left to speak, or even to answer upward?
The fact is, no one. We end up with a situation in the church a lot like the situation in the secular world. Those who are sent to the capital as representatives of "the people" end up in love with the perks and prerogatives of being above the hoi poloi, they love people beseeching them for favors, and that's what they end up seeing as their job. They stop seeing themselves as spokesmen for the collective rights of the body politic, which each constituent holds as a personal possession. Instead, they find themselves in the position of benefactors. They have become representatives of what is "above" to those who are "below." And no one is the voice of the people.
Elders of the church are the people's representatives, to sit with the ministers (be that in on a session, where they typically dominate; or in Presbytery where ministers in the OPC tend to dominate, or G.A. where there is a form of parity in the OPC) and come together as representing above and below for the sake of good order and discipline.