This exactly. There may well be a need for improved efficiency, but that's not achieved by firing people at random because they haven't responded to an email. It needs someone to take the time to establish what the department's role is, who does what, what could be done better etc.
You don't just go "That department has 100 people but they only need 20" and then fire 80 people at random. You ask what the "extra" 80 people do (maybe 20 people could manage the job if they had the exactly necessary set of skills between them, but chances are they don't; you may need 40 people just to get the basics covered. Then you need people for when those people are off sick or on holiday, or when the workload suddenly ramps up; you need people with experience who know what to do if some disaster happens; you need people who keep an eye on how things are being done and to continually suggest improvements (eg looking into new technologies which become available), etc etc).
It's a bit like suggesting that the local fire station only needs 5 firefighters rather than 30 because last week there were 2 fires and they only needed 5 firefighters for each one.
Yes, there are probably some people who do very little day to day whose jobs could easily be cut, but it may well be a lot fewer than someone from the outside would think.