Community shield was played at the Old Wembley from 1974-2000. Then Millennium Stadium 2001-2006, and from 2007 onwards at New Wembley, other than Villa Park 2012 due to the Olympics, and King Power 2022 due to the Women's Euros.
So neither of you are quite right. Obviously early 1970s is nothing like "the dawn of time", but it's also three decades prior to the closing of the Old Wembley. It's been held at both iterations of Wembley for a total of 43 years, with the interregnum period being at the Millennium Stadium.
Having it at the national stadium makes it neutral, and also puts it on an equal footing with the majority of national Super Cups. It'd be hard to say it wasn't a tradition at this point, but apart from that it's also the most fair way of doing it.