As I recall, the reason Angels are depicted (or visualised) with wings is because they are spiritual beings & travel 'vertically' (speaking metaphorically) between Heaven & Earth.
The Valar & Maiar, having entered into the World, are bound within its circles, & are unable to leave it & return to 'Heaven' as long as it exists. Hence, no wings.
Which brings up the question of whether there are any equivalents of Angelos within the Legendarium - spiritual beings who travel between Illuvatar & the Valar/Eruhini.
This is interesting - for me at least - in that while Tolkien describes the Valar & Maiar as 'Angelic' beings & speaks of the Istari as 'incarnate Angels' they have very little in common with Biblical Angels. Basically, they are the Pagan gods by another name & exist within the world - hence, no wings, as they do not pass out of this world into a 'higher' one & back. Hermes is a different case, as his 'wings' are on his heels, not his back, & merely permit him to move around with speed, not to fly.
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