First, I cannot grow trees in my small rented flat. And felling trees and turning them into paper is quite a hard work, it's only cheap at an industrial scale and it kinda fucks up the environment a bit. Paper used to be an expensive commodity (people would wrote letters like this).

The properties that make gold expensive are its limited supply, as you pointed, and the fact that it doesn't degrades with time, which make it a great material to use to 'store value'. It has some other interesting physical properties that make it useful, but those aren't the main reasons of its price.