As you rightly say, angels are often said to wear white clothing.
Matthew 28:3 His countenance was like lightning, and his raiment white as snow
Mark 16:5... a young man sitting on the right side, clothed in a long white garment; garments white as snow...
Luke 24:4... two men stood by them in shining garments:
John 20:12... two angels in white sitting, the one at the head, and the other at the feet, where the body of Jesus had lain.
Acts 10:30... behold, a man stood before me in bright clothing,
We are not told why they wear white.
We are told that white represents sinlessness.
Psalms 51:7 Purge me with hyssop, and I shall be clean: wash me, and I shall be whiter than snow.
Isaiah 1:18 Come now, and let us reason together, saith the LORD: though your sins be as scarlet, they shall be as white as snow; though they be red like crimson, they shall be as wool.
And that white clothing represents righteousness.
Revelation 3:4 Thou hast a few names even in Sardis which have not defiled their garments; and they shall walk with me in white: for they are worthy. 5 He that overcometh, the same shall be clothed in white raiment; and I will not blot out his name out of the book of life...
Revelation 3:18 I counsel thee to buy of me gold tried in the fire, that thou mayest be rich; and white raiment, that thou mayest be clothed...
Revelation 7:14 And I said unto him, Sir, thou knowest. And he said to me, These are they which came out of great tribulation, and have washed their robes, and made them white in the blood of the Lamb.
Revelation 19:8 And to her was granted that she should be arrayed in fine linen, clean and white: for the fine linen is the righteousness of saints.
At the transfiguration Christ’s clothing became as white as light.
Matthew 17:2 And was transfigured before them: and his face did shine as the sun, and his raiment was white as the light.
God is light and dwells in light and light is connected with immortality.
1 Timothy 6:16 Who only hath immortality, dwelling in the light which no man can approach unto...
Moses’ face shone with the reflected Glory of the angel who gave him the Law and spoke with him face to face.
Exodus 34:29 And it came to pass, when Moses came down from mount Sinai with the two tables of testimony in Moses’ hand, when he came down from the mount, that Moses wist not that the skin of his face shone while he talked with him.
2 Corinthians 3:7 But if the ministration of death, written and engraven in stones, was glorious, so that the children of Israel could not stedfastly behold the face of Moses for the glory of his countenance; which glory was to be done away: 8 How shall not the ministration of the spirit be rather glorious?
White clothing which emits light would seem to be an aspect of the glory of those possessing the divine nature.
2 Peter 1:4 Whereby are given unto us exceeding great and precious promises: that by these ye might be partakers of the divine nature, having escaped the corruption that is in the world through lust.
The promise is that those who believe the gospel and are baptised into Christ will be raised from the dead and made equal to the angels when Christ returns.
Luke 20:35... they which shall be accounted worthy to obtain that world, and the resurrection from the dead, neither marry, nor are given in marriage:36 Neither can they die any more: for they are equal unto the angels; and are the children of God, being the children of the resurrection.
Colossians 1:12 Giving thanks unto the Father, which hath made us meet to be partakers of the inheritance of the saints in light:
We might conclude that angels wear white because they are the messengers of the God of righteousness and they possess the divine nature in which his glory shines forth..
I hope you have found this helpful.
May God bless you,