Sure it can mean space. I disagree that the only reason to want more space is to hold more stuff. I want more space so that I can have a room that I can close the door on and call my own (and by extension let my daughter and girlfriend have their own rooms as well). I'd like rooms with dedicated functions like a workshop for me to build things in and a room where my girlfriend can paint. I'd like a guest room so I can have friends stay the night without being forced to sleep on the couch in the living room. I'd like a small garden so I can grow food and cook outside.

Now as it stands non of these wishes have become important enough for me an my girlfriend to give up the city, and they are all 'problems' that can be worked around, but there are more reason to want space than simply to store things