Maybe give the power/obligation to the "engineers" (well, here it's about universities, but I know far more about managerial duties of engineering associations

Maybe give the power/obligation to the "engineers" (well, here it's about universities, but I know far more about managerial duties of engineering associations than of a university; though much should translate), which can pawn off the non-engineering work to some sort of group-shared secretaries. I.e., the managers aren't the ones owning the power, but the engineers are. The latter just don't want to do the daily tasks that require holding the power, so they hire a delegate to hold the power and take care of day-to-day duties. And because each "engineer" doesn't have enough non-engineering work to keep their own secretary occupied during the times of day the secretary needs to be available (for answering phones, interacting with the "engineer", etc.), groups of engineers come together and hire a small team of secretaries to keep up the availability even in cases of sick days. Small team as in, like, on the order of 3-7. Given their already-required organization skills, a flat hierarchy among them with escalations directed to an elected board of "engineers" should suffice, giving a natural damper on secretary team size due to scaling limits of such a flat hierarchy (and organizational charta/codebook restrictions that prevent any middle manager/secretary-overseer from holding actual power). I'd actually be happy to hear about the practicalities of such a structure for an engineering collective/organization (lacking any sort of CEO presiding over the engineers)...