I see it more like a conventional fashion thing; with big (?) backpack you are supposed to wear boots. If you are "backpacking" around the world you are supposed to wear boots. Which means you will be carrying the pack about 1% of time of your trip, but you are stuck with the heavy boots 100% or the time, either wearing them as the only footwear even in the tropics, or carrying in/outside your pack when you finally realize you can use sandals…
I do not buy the "ankle support" theory. Light shoes, ideally trail runners, are so much more nimble and grippy that you are much less likely to twist your ankle in the first place. What comes to Everest and joggers, I climbed to Camp 1 on the West ridge route (Lho La pass to Tibet behind EBC) with Adidas Oregon trainers in -85… The American team had Nike high top joggers of the same vintage. Certainly for the upper camps they also had Koflach plastics.