I wouldn't say "no Balrog ever could possibly have had wings", but rather "Tolkien never described any Balrog having wings".

The only mention of wings on Durin's bane is an obviously non-physical simile comparing the movement of the expanding shadow at a specific moment to the general shape of wings, and the simile becomes a metaphor in the next paragraph for greater effect (and to avoid repeating the simile, which would be quite tedious). Tolkien uses the same process in the Akallabêth (first, the clouds are described as being shaped like eagles; then, the same clouds are referred to as "the eagles").

Now if we were to consider those wings as physical, there would be a huge problem in how Tolkien describes distances and measurements in the Balrog scenes. You'd have to imagine a ~5m tall Balrog (uppermost estimation) with a ~50m wingspan (lowest estimation), making the Balrog's visible shape composed of around 90% wings 10% body? And yet Tolkien's descriptions of Balrogs fully concentrates on those 10%, consistently calling them humanoids/of human shape, with the mention of wings left vague at most. Not to mention the obvious conclusion that wings that big would be the worst, most impractical thing ever.

Also, as far as I remember the description of the Balrog being able to go out of the chamber of Mazarbul, you'd need that Balrog and its 50m wingspan to go through a doorway small enough that a normal man can easily push the door closed in one movement, as shown during the earlier battle. When you pay attention to the description, what Tolkien focuses on, and the measurements, Durin's Bane being winged doesn't make any sense, and it's the reason why that debate only exists among fan (particularly Jackson fans) - all the scholars I've seen talking about the topic are unanimous that there's no actual wing being described.