The "support your feet" argument came from the belief that everyone is supposed to have a prominent arch and that shoes could force your feet into that shape, but as far as I knew had been thoroughly refuted over the past 15-20 years. Forcing your feet into having an arch when it's not your natural form can actually cause problems further down the line. Soles not being flexible also changes how you use your ankle and IIRC how you balance while walking, possibly contributing to back problems.

Keeping your feet clean and protecting them from surfaces are the primary purposes of shoes. Some people need them for support after having worn shoes too often (my parents are in this situation and have a separate set of "indoor shoes" just for this), or some sort of disability that needs those super-wide-sole shoes, but in general they are not for supporting your feet.