Presbyterians do not, of course, have bishops. We are very decidedly non-episcopal. The presbytery is an ingenious republican arrangement to accomplish most of the functions of a bishop, without the authoritarian dangers.
However, there are a few things that bishops do, when they are functioning well, that presbyteries cannot accomplish. A good bishop knows the people in the diocese and has a personal relationship with at least the leaders of the congregations. The presbytery is not well-designed for the person-to-person actions of bishops.
A presbytery, as a republican organization, always needs to be finding the right person for the next job. This is especially important in getting the right mix of pastors and elders to staff the crucial committees and oversee the vital ministries of the presbytery. What a presbytery needs is someone in a position to have a wide range of contacts over the several congregations of the body.
The Presbyterian bishop needs to be chief talent-spotter.
Since the presbytery needs someone to accomplish this function, we keep growing some kind of talent spotting system. This is often jury-rigged and haphazard, depending on the personal contacts of the chair of the nominating committee as much as anything else.
I believe presbyteries should be smaller and more organically connected than they now are. This would go a long way to bringing the people doing the calling in touch with the people who should be called.
At the same time, I think a modest Executive Presbyter role is a useful one to the presbytery. Small presbyteries may not be able to afford full time executives. In that case, I think right-sized presbyteries trump the need for a dedicated executive. Even a small presbytery, though, should be able to afford part of someone's time -- perhaps the pastor of a smaller church, or a mostly retired person, or someone with a well-employed spouse -- to be the connector.
Perhaps what we need is not a Presbytery Executive, but a Presbytery Maven. Or Presbytery Magpie.