...Do conditions exist in this part of the Sierras to hypothetically allow for a snow-covered Main Trail all year around?
No. Temperature and elevation are some of the reasons.
If conditions existed for snow all year round, then we won't be having a burger, fries, and beer at the Portal Store between May and October of each year.
We would be parking at Lone Pine Campground and hike the "main trail" with LPC's Whitney Portal National Recreation Trail as the TH. Just like in the old days.
Now, unless Hell or Lone Pine freezes over (whichever comes first), it ain't gonna happen.
Have fun.