Way too long for a comment, but perhaps useful...
[T]here are languages, such as Arabic, Malay, and Urdu, where /h/ can occur at the end of syllables, e.g., Malay basah /basah/ "wet". Notice that, in analysing syllable structure, we are talking about sounds (phonemes); the spelling is irrelevant. Thus, while many English words end in an h letter, this letter never represents an /h/ sound. It may be silent as in messiah, cheetah, or [...]
From: The Handbook of English Pronunciation by Marnie Reed and John M. Levis
Note that bahasa Indonesia has citah for cheetah.
Messiah is interesting:
The modern English form represents an attempt to make the word look more Hebrew, and dates from the Geneva Bible (1560).
From: Online Etymology Dictionary
As can be seen at TheFreeDictionary.com, many, if not a clear majority of, English words ending in ah seem to originate from the Middle East or the Indian subcontinent or even further east. However, many more English words end in a. It seems that only words from those regions are likely to be transliterated to end in ah.
According to The Gem Set in Gold: Dhamma Chanting, English translation with Pāli & Hindi by S. N. Goenka:
ḥ is an aspiration following the vowel, e.g., aḥ is like 'uh'. [Hindi only, not Pāli. And the ḥ is also a vowel.]
So, here's a theory: It started with the spelling Messiah and then (English-speaking) people just started using that spelling for all kinds of words (with such aspirations, locally) from those regions.
If this would be true, it would be a nice connection to OP's other interest.