It is a known fact of countries across the pond, either way, that "shall" preoccupies either the dusty volumes of ancient literature or living, breathing if formal parlance. Where one would be derided as pompous in the other, it is hardly noticed. I shall nevertheless try and spell out the rise of not just deontic - pertaining to duty - and futural shall and should, but also to its fall amongst World Englishes in favour of that (or those) modal verb of volition will and would, as well as the rise of going to and all its progeny.
Part I - Of Owing and Willing.
Back in Old English times, mainly the 7th century, what was to become the modal verb shall was originally a verb meaning to be indebted, to owe someone a favour (whence our ought stems as originally a past tense) and in general thus being obliged to return it.
Swá sceal geong guma góde gewyrcean
fromum feohgiftum on fæder bearme
þæt hine on ylde eft gewunigen
wilgesíþas þonne wíg cume·
léode gelaésten: lofdaédum sceal
in maégþa gehwaére man geþéön.
(Beowulf, lines 20 - 25)
So ought a young man by doing deeds
Grand gift-giving on his father's lap
That him then in old age, again remain,
Faithful friends when war comes
People serve (him): glory-deeds must
In tribes and people everywhere thrive.
We therefore see that Old English sceal performs the task of an ordinary verb rather than a mere modal auxiliary verb. Hence in Danish the word skulle ("should") is etymologically related to skyld ("guilt") - since one feels as if it is a personal matter that you owe a person something. As mentioned, in a similar vein ought derives as the older past tense of owe thus the deontic, grammatical term for modal verbs and constructions implying duty or obligation, aspect derives from the same sense of owing someone something or having to return a favour. The Proto Indo-European etymon of shall is *skel(o) meaning "guilt, blame."
Likewise, "will", both the verb and the noun denoting actions appertaining to "volition" or "wish" stem ultimately from the Proto Indo-European *welh meaning "to choose, to want", there is therefore a strict contrast even in ancient times between one term, shall, referring to owing someone the favour or feeling indebted thus prompting one to perform an action to repay it and vice versa, will, one that is not bound by obligation, but by volition which therefore also infers choice and selection.
One might say that "will" therefore as a modal verb at its most basic level is less binding than that of "shall." Speaking of not just the two words in the context of their English descendants, but also the rest of the Germanic languages in terms of where their usage is continued to be used as indicators of duty and volition - in addition to auxiliary markers of the future tense.
I wil syster that ye wete he is a ful noble knyȝt.
"I will sister that ye know that he is a fully noble knight"
Le Morte D'Arthur, VII.
Here "will" expresses its most basic aspect of willing, wishing or wanting to do something, we might in English instead rephrase it as "I want you to know, sister, that he is a wholly noble knight", where "want" has replaced the Middle English modal verb in its sense wishing or wanting something of someone.
We seen still this aspect in Danish, where the quote can be translated as "Jeg vil gerne have at du skal vide at han er en komplet ædel ridder." What is worth noting is that the adverb "gerne" (to want to, to be desirous of doing) is added to strengthen the aspect of the speaker's desire to inform the interlocutor, his sister, "at du skal/bør vide" is added as a subordinate to strengthen the informational aspect of the sentence, but it is nevertheless proof that this ancient usage has not fully become obsolete in Germanic languages. It is possible to render it as "Jeg vil (at) du ved (at) han er en helt (igennem) ædel ridder", but this can sound archaic hence the adverbial verbs needed to render it in a more modern register.