What time did people still write "cometh" and so forth?
WOuld edgar allen poe still have written "cometh" or was it all "comes" by his time?

According to Early Modern English,+ +-eth+ began to be supplanted by +-es+ by 1500. "As early as 1500, there is evidence for its use in familiar speech even in the London area, and in the course of the 16th Century it became the normal spoken form." +-eth+ was probably still used in "formal and solemn speech" however, and poets (such a s Shakespeare) used it for rhythmical purposes. +-eth also continued in writing for the first half of the 17th century, but there is evidence that the written form was expected ot be pronounced "es." By 1700 it was rare except in poetry.
Doth that answereth thy query?

Poe might well have used it if he needed the extra syllable. He used "quoth" in his most famous poem and that was certainly long dead in ordinary speech and writing by his time.
The -s shows up in the North long before 1500.

It turns out he used it at least once, and in prose. Here. But it's a demon speaking, and like most demons he speaks archaic English.
By the way, Poe's fable takes place "in LIbya, by the borders of the river Zaire."
Which reminds me of Manon dying of thirst in the deserts of Louisiana.
Poe might well have used it if he needed the extra syllable. He used "quoth" in his most famous poem and that was certainly long dead in ordinary speech and writing by his time.
A potentially misleading example. Just to be clear (as #2 probably knows) "quoth" is an archaic past tense (of a Middle English verb "quethen"); "cometh" (and its ilk) is an archaic (3rd person singular) present tense.
As #1 points out, by the 19th century, poets would have used the form only if deliberately trying to sound archaic, like Tennyson in "Mariana":
She only said, 'My life is dreary,
He cometh not,' she said;
She said, 'I am aweary, aweary,
I would that I were dead!'
#3, Act III, Scene 3 of Shakespeare's Winter's Tale is set in Bohemia, a desert country near the sea.
I forgot to mention: Originally -eth+ was southern and +-es+ was northern dialect, hence the note that +-es was used "even in London." Usually London dialect prevailed, but there seems to have been a pronunciation change or rather a change in preferred pronunciation to drop the volwel sound in the suffix. For instance, thinketh was reduced to think'th or thinkes to thinks--and it's a lot easier to say "thinks" than "think'th." So the northern form prevailed.

thanks for all the useful explanations.
and interesting to see how this thread took a travel-turn (as about bohemia on the river zaire).

Thou+ did a quick turn to +you too during this disruptive (evolving) linguisic period for the English language.
Shakespeare did many a thou+ and +you alternatively during the wiritng of his plays over this period...
The "thou didst" era was clearly coming to a close, if not already closed, during his writings...
However... the only condition he was under was not to involve the Tudors in any political sense in his plays.