Some working styles are difficult to accommodate. Staffing plans that don't have clearly delineated responsibilities, very last minute requests from people who didn't plan ahead. Some people avoid working at all costs, knowing others will take it on for them, contributing to burnout and uneven workloads and even more last minute requests. Some processes also get held up by extremely small details, with very little benefit for doing so. Probably not enough payroll dedicated to administrative staff who could handle some of the smaller details that are necessary. However, some people are challenged to delegate anyway.
You have to know who to minimize contact with — there are a few people who might not have job security at other places.