The echo area is the line at the bottom of Emacs below the mode line:
                     ~                       ~
                     |                       |
                     +-----------------------+
                     |-U:--- mode-line       |
                     +-----------------------+
                     | M-x echo-area         |
                     +-----------------------+
Now the mode line is highly customizable while the echo area is more rigid (and unused a lot of the time). The question is pretty simple: is it possible to hide the echo area during inactivity and redisplay it once it needs your attention:
  ~                       ~             ~                       ~
  |                       |             |                       |
  |                       |             +-----------------------+
  |                       |             |-U:--- mode-line       |
  +-----------------------+             +-----------------------+
  |-U:--- mode-line       |             | M-x echo-area         |
  +-----------------------+             +-----------------------+
          Inactive                                Active
This is similar to the way Google Chrome displays URLs when you hover your mose over a link and the Firefox addon Pentadactyl where the command-line is hidden by default.
                        
As far as I know it's not possible to hide the echo area, and I would not agree with you that it is unused a lot of time. From buffer switching over M-x commands to minibuffer output, a lot of different stuff goes on in the echo area.
I can understand that on small displays, e.g., on netbooks etc. it is desirable to save screen estate. But I would argue that the echo area is used much more when you edit a file than the address bar of a web browser is used when you look at a web page. It's an integral part of Emacs.