Agree with @cinnamon1212 and @cameo43 about the HOS of Millbrook. Really great communication skills with parents and puts parents at ease. When our friends dropped their child off at Millbrook several years ago, he gave them his cell phone number and told them to never hesitate to call.
We are living in a different world and with different expectations than a decade ago - even a year ago! I think the effort made by any HOS during this time of virtual visits and virtual fund raising will be an important test of one’s communication ability and leadership style.
I believe the demands placed on any HOS has changed over the past decade, and will continue to change. There are huge issues related to finance, legal issues, equity, and long term sustainability. As @Publisher mentioned, sometime avoidance by the HOS may be what the Trustees had dictated. For example, if your school has a new HOS and must travel the country to meet & greet. Another scenario, is BOTs using the HOS to fund raise for a new initiative or building.
To add onto what @cameo43 posted above, there are some HOS that seem to hang out (hide?) in their offices a lot - or are just not engaged with students. Maybe they are financial experts or concerned with hands-on management issues, rather than engagement with students.
If you have an active - “working the room” - engaging Assistant Head of School or Academic Dean on campus who is genuinely involved with student life on campus and/or teaching , then an important need is fulfilled. Some parents seek that out in a school.
In listening to conversations between my kiddo and students from other schools over the past several months, it seems that they want a HOS with strong leadership qualities and who is engaging. This COVID crisis has been a difficult test in management, communication, vision, and leadership for any HOS. Leadership is very much needed during this time of uncertainty.