Blizzard explain why adding more space to the stash isn't a trivial matter and how the stash and player interaction systems are connected.
Turns out they can't easily add more stash tabs as the game pulls the entire stash for every person you encounter. This leads to memory and performance issues. They need to fix this before they can add more stash tabs.
Yeah, seems odd. For other characters, loading their stash space (or heck, even their inventory) doesn't seem necessary at all. I know you can inspect other players but that only shows equipped gear.
The only thing I can think of is that it's something to do with trading...?
Option 1: Create complicated system which loads information about other players on demand, being careful that certain information must always be preloaded before it is needed to prevent lags, while different information can wait for a network request. Must consider the implications of increased network chatter on server load.