A/an indefinite article

The rules that developed for writing grew out of how ENLs spoke. We follow rules of phonology, not prescriptions.

CGEL: The choice between 'a' and 'an' depends purely on the phonological context. The liaison from [an] occurs before a vowel sound, not before particular letters.

This is unproblematic as far as speech is concerned, but in writing the status of expressions like ... is less clear.

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They point out that words like, habitual/heroic/historical/hotel/hysterical are examples that, when spoken in isolation, all have initial /h/ sound but it is unstressed. When we use these words in context in speech, we often get, for example "an abitual criminal" where the /h/ is lost.

Doesn't this also vary upon the dialect of English that is spoken in any particular region?  For example, where I live the H in historian and hysterical is stressed, therefore, these words would be preceded by the article "a" instead of "an."  So, is it possible that either one is correct based upon regional dialect and whether or not the H is stressed or unstressed?

both of them are correct the first answer is the general rule the second is the exceptions