An aspect that has not, not my knowledge, been previously mentioned is that of the balrog's long sleep. Two factors would contribute to the theory that it had wings, yet did not use them. For one, we all know that neglect and disuse produces atrophied muscles. After centuries, even ages of hibernation, the balrog was not able to move its wings because the muscles had deteriorated.
The second aspect is that which Shakespeare called "to sleep, perchance to dream". Dreaming for such a long time may have caused the balrog to forget that it had wings. We all know how disoriented we can be when rudely awakened out of a dream! By the time it remembered its wings, and the additional time it took to remember *how* to use them, it failed miserably because it *could not*.
All further posts and arguments are redundant: the mystery has thusly been solved.
Thank you - really, applause is not necessary.