The power of a school's brand

As a parent myself, I sometimes wonder if schools realise quite how powerful their brand is within this specific sphere of their target audience? Anything that carries the school crest (or perhaps logo is more fitting) automatically gets my attention. And if you are a parent, it is quite an interesting mental exercise to think how this compares to some of the other brands we see every day.
I struggle to think of any brand, in any sector, that prompts quite the same response in me, as seeing the crest of my children's school. Obviously, this is because I am very interested in anything to do with my family. I can hear many headteachers, school business managers and teachers out there thinking, "ah, but our parents are not like that". Maybe the headteacher of my children's school would say the same thing?
So how can schools take advantage of this? Undoubtedly, a number of ways but the one that always springs to mind for me, is push notifications. How many times a day do you look down at your phone when you hear a little 'ping' and you see the icon of the app that has triggered the alert? I may choose to ignore some, but I never see the school crest without checking the alert. I think this offers some exciting possibilities for schools and their school apps.