Your will shall be done
In this case, it will not only mean future time. Shall has a shade of promise, guarantee, not just "Your will will be fulfilled", but "Your will will be fulfilled", "I promise that your will will be fulfilled". It also corresponds to a more formal, formal style of speech.
It has nothing to do with (in particular) illiteracy and (or) simplification of grammar in American English. On the contrary, the usage shall be characteristic of good British English.