If you get specific enough about the region (e.g. region within a region), I could see regions working.
I don't think my idea is that unworkable, though. Most teams are in specific cities and those that aren't can just pick any city in their league's region to be close to, it would be publicly visible, and it couldn't be changed (unless a new owner changed the city, and that might only be allowed in the offseason, and once per owner).
But to get simpler you might have regions like "USA Southeast," (basically anywhere there used to be slavery) with a climate based on Atlanta, "USA Northeast" based on New York, "USA Midwest" based on Chicago and including anything north of the Confederacy and east of the Rockies, "USA Southwest" based on Albuquerque, covering California, Arizona, New Mexico (using Albuquerque as it's less extreme than Phoenix but more extreme than the West Coast).
The rest of the USA could fit into general regions that would cover areas through the world:
"Mountain," including all the world's areas that are basically mountain climates based on something like Cheyenne, "Maritime," based on Seattle and also including places like London as well as the Pacific Northwest, "Arctic" for northern Canada and Alaska, plus much of Russia, and places like Sweden, maybe using Anchoarge, "Tropical" with San Juan as a basis that would include all Tropical areas, and then for Europe, "Continental Europe" (using Berlin) for most of it with "Mediterranean Europe" (using Naples, Italy) for that close to the sea, with the aforementioned "Maritime" covering England, Ireland, etc..
"Sahara Desert" (using an Ethiopian city) could cover northern Africa, with Johannesburg covering "Southern Africa."
One city like Sydney could cover Australia and New Zealand, and I could see Seoul covering Southeast Asia, although I'm sure there are some major differences in climate within the region that I don't know but someone who knows the region better would.
That's most of the world in maybe 15 climate types. I'd gladly just use Koppen classifications, but that would confuse people more.
I think we need something at least that intricate (either regions like I described or Koppen classifications, or my original idea), though, to make the weather not ridiculous for the areas.