I think the size of the school matters in terms of you/your child getting to know the HOS. At larger schools you might not see/interact with the HOS but at smaller schools, you likely will. Small schools have smaller communities and the HOS is often involved in a number of things from fundraising, to arts and sports events to major events. I agree the HOS needs to be able to get to know parents and kids and to be able to fundraise as well. At one school, the HOS often sends nice emails about specific things. IMO, having an approachable HOS is a major positive.
One thing that turned us off at one school was the obvious fundraising efforts but lack of social efforts. Seemed the HOS was friendlier to some than others. Not a good look. It felt like being invited to that party where you know it’s a social clique and even though you are included, you know others may not be. Not my scene at all.