The periodicity reflects the allowed solutions to the Schrödinger equation for electrons in atoms. It is not some branding teams' genius design innovation.

Ironically, you are in a superstate between "can" and "should".

It is _also_ a colorful collection of boxes that a billion+ people could instantly identify.

Cashing in on that global cultural awareness is just the kind of innovation a genius branding team needs.

It does annoy me when 'Periodic Tables of X' are just lists of color coded boxes, but I get it.

FWIW, there are other styles which emphasise other aspects. https://en.wikipedia.org/wiki/Types_of_periodic_tables