OK not the best public service announcement...
One of the problems with labeling every square is that the pieces would cover the names. They could then add some kind of light-up thing but that would probably just distract you.
I learned the coordinates fairly easily because I learned otb and we had to write the moves down when we played. Maybe you should read some annotated games. That way you'll get familiar with the squares while learning and at your own pace.
http://www.internetchess.com/columns/amartin/150barry.shtml
http://www.tim-thompson.com/gaprindashvili.html
http://main.uschess.org/content/view/10115/341/
So apparently it's dumb idea Don't know but I was playing chess for several years now casually and still have very hard time keeping with moves when high level player commentates or describes the game.
And for someone who said it would waste a lot of memory, ar you serious? :D How can some numbers on the board make any significant different, especially considering that 90% of users probably would not be using it.
Next after you learn the coordinates you will asking which opening is better and refuting the move orders or a move itself to play using it or against it. Guess which part we like to talk about here?
Did you not read the last part of my comment. Save you and us time and learn it without needing the marks on each square. Practice it. Spend your time and energy doing it. As you can see it is creating a barrier between you and most of us which does not have to there. It is your choice to work out. But if you do not overcome this then your enjoyment which even you have to admit will be limited at chess.com.