In the real world, no clergy can actually cast spells, so of course being in charge of a church is administrative. But in a world where there are spellcasting clergy, I have zero reason to believe that mere non-spellcasting administrators would be put in a position of authority over them.
We're certainly threadjacking here, but while I can see your point, it seems to apply only when "ability to cast spell" directly equates with a special favor from the gods. There is no reason to assume that a church with very active gods wouldn't have them directly intervene and say "you, you're a miracle worker, while you, over there, you'll take charge of making sure my churches are managed well". Make an analogy with engineers and highly qualified technicians. They have "powers" that managers don't have, and generally, when promoted to management, it doesn't work very well and not everyone of them is happier (because sometimes you
want to be engineer, not a manager). In real life, appointment to position is... organic at best. In a church with an active voice of the gods, the god-appointed Manager will have every reason to hold authority over the god-appointed miracle worker. As an analogy, the Pithyas in Delphi (indeed a divine spellcaster) weren't in charge of the temple of Delphi. Their qualification (uneducated celibate girls of low-class origin) was extremely different of the qualification needed for an administrative charge. I would say that a fantasy church with an easy access to divination spell would ensure, when they select a new High Priest, that their choice is god-sanctionned.
I'd say its heavily setting-dependant: in "silent gods" setting and in "very talkative gods" settings, I think my version would make sense, in "intermediately silent gods" settings, where the ability to cast spell is the only sign of a special link to the god, yours would make sense, as people would be awed by the spellcasting ability.
I hear that you say that IRL the church-leading business is administrative since there is no competition by spellcasters and you're right, but it's a job nonetheless, a full time job that wouldn't necessarily intersect with other jobs of equal importance. Doctors don't run hospitals [well, maybe in the US they do since apparently House MD's hospital is run by Dr Cuddy, but it's not true everywhere]. If one was given the power to bless crops and heal the sick, you'd want them to be doing that full-time, not just on Friday morning from 10am to 12am, with the rest of the week spent doing high-level management work.