Look at the etymology of both words:
spirit's is: Middle English spirit, from Latin
spīritus (“breath; spirit”

. Compare
inspire,
respire,
transpire, all ultimately from Latin
spīrō (“I breathe, blow, respire”

. Displaced native
Middle English gast (“spirit”

(from
Old English gāst (“breath, soul, spirit”

).
ghost's is: From Middle English
gost,
gast, from Old English
gāst (“breath, soul, spirit, ghost, life, mind, angel, demon, man, human being”

, from
Proto-Germanic *gaistaz (“ghost, spirit”

, from
Proto-Indo-European *ǵʰeizd-,
*ǵʰizd- (“anger, agitation”

. Cognate with Scots
ghaist (“ghost”

, West Frisian
geast (“spirit”

, Dutch
geest (“spirit, mind, ghost”

, German
Geist (“spirit, mind, intellect”

, Swedish
gast (“ghost”

, Sanskrit
हेड (heḍa, “anger, hatred”

.
((All information from the links given above))
English borrowed words from the Latin; it is what made middle English develop from old english; the Norman conquest triggered a lasting change in the English language, infusing Norman and Latin elements into the Anglo-Saxon base.
Furthermore, we can see that the end etymology of ghost is not only more ambiguous but has interestingly always included the idea of something
supernormal, sometimes even with a negative conotation (especially the very root of Indo-European).
On the other hand spirit is actually more direct, not to mention given its ecclesiastical nature from the Vulgate, making it a great translation, given the ancient Hebrew and early Christian concept.
In addition, note the words "displaced native."
When kids go out trick-or-treating on Halloween and say they are going to dress as a ghost, they aren't dressing as the rational aspect of the soul which connects us and allows us to have a relationship with God; they are going as a disembodied boogieman (or boogiewoman) to haunt and spook, which fits the historic use of ghost, given above, rather well.
We speak modern English, not middle English, where the changes began, nor early modern English, the last gasps. The etymology is clear and so is the common use of the language in most of the English-speaking world. The Article of Religion in question is most certainly therefore in play.
That isn't to say that
private liturgies, such as collegiate or seminal, must align. Rather, when the people worship, the language must be in their tongue. No one speaks English like that anymore. However, if an ordained priest and some of his or her friends were to meet for a liturgy outside the main Sunday one for all, and they did understand a different language, then Anglican orthopraxy allows a different language. After all, there was a Latin translation of the 1559 which was popular in certain circles, but those liturgies were attended by those who understood Latin.