Just got to the end of the game and didn't want to do that battle on the tiny map against the final boss, went to do the other, thinking there'd be more stuff to do up in the desert.

Nope... it's game over, you ran away. :-o

So what's that huge desert area on the right used for?

Very minor spoiler:
[spoiler]Some sidequests in NG+.[/spoiler]

Ah I see. Thanks! :-)