True, flightless birds do have wings, but that is because they evolved from birds that could fly and they still have wings although they are now useless. Since balrogs were maiar and did not evolve their form, but instead took their form themselves, I do not see the point in having wings that they cannot fly with and would be without a purpose.
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His sword was long his lance was keen
His shining helm afar was seen
The countless stars of heavens field
Were mirrored in his silver shield
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