It is the most famous shakespear quote in german. Close to 100% of germans will have heard the name shakespear, and probably 80% of them will know nothing more about him save for that quote, and almost everybody will make the association to shakespear whenever someone says "...Das ist hier die Frage" in any context whatsoever. So it's a possibility.
It's also about the most famous Shakespeare quote in English.
It kind of sounds wrong with anything more than "that is the question" to me, and I'm not really familiar with blank verse as poetry, so I don't have enough of a sense for how it's supposed to sound metrically to be bothered by the meter being perturbed by a missing syllable (plus, I think there may be intonation and thing changes between Shakespeare's dialect and my own that disrupt the meter). So the natural way for me to translate the line is without "hier".
But both the English original and the traditional German translation have exactly 11 syllables, so "originally done for meter, now tradition" is probably the answer.
I think there may also be some conflict between the cultural norms for European poetry vs. the natural timing structure of the Germanic languages that's causing my brain to prefer a rhythm that's less poetically "correct". The concept of meter we have in the modern West is built on poetic forms that originated with the mora-timed classical languages and continued in their syllable-timed descendants. But the Germanic languages are stress-timed (stresses are approximately evenly spaced, and intervening unstressed syllables are rushed), and in their native poetic forms (now rarely used), unstressed syllables don't count in the meter at all (there can be any number between two stressed beats):
BA-ba BLACK sheep HAVE you any WOOL?
YES sir, YES sir, THREE bags FULL.
ONE for my MASTer and ONE for my DAME,
and ONE for the LITtle boy who CRIES down the LANE.
we HEARD the HORNS in the HILLS RINGing
the SWORDS SHINing in the SOUTH-KINGdom
STEEDS went STRIDing to the STONing-LAND
as WIND in the MORNing. WAR was KINdled.
So if you're used to an English original like this:
to BE - or NOT - to BE, - THAT is - the QUEStion
The "poetically correct" way to translate that to German is maybe to rearrange the metrical feet a bit, but to keep the same number of syllables per foot:
SEIN od - er NICHT - sein, DAS - IST hier - die FRAge
But to someone whose two best languages are Germanic languages who lacks a literature degree, this may sound like a more natural translation:
SEIN - oder NICHT - SEIN, - DAS ist die - FRAge
And they may interpret the metrical structure of the original somewhat differently:
to BE - or NOT - to BE, - THAT is the - QUEStion
The only difference is in the arrangement of unstressed syllables in the first half of the line, which get glossed over in stress-timed languages.