Why does God use an army of Angels to fight against evil when he could do it himself?

God uses angels for this heavenly battle because he is in his rest day, the seventh creative day, which he ordained as holly and a sabbath. So his angels have carried out his work. He couldn't break his own law that he expected man to follow.

The fact that God comes with an army of angels represents unanimous agreement in God's justice in His treatment of sin. God desires His creations to be His co-workers, serving Him with intelligent appreciation of His love and justice, not in fear and doubt of His decisions.

In reality it is hardly a battle with these angels reflecting the glory of God, with countenances as lighting and robes as white as snow (Matthew 28:2). If a man can cast out demons in the name of God (Mark 16:17), how much more can an angel? If anything these battles represent God's army standing in unity against the ideologies and accusations of Satan and his legion, knowing them for the lies that they are.

God is about wrong and right and the struggle between them. We assume God is almighty, but maybe he needs some faith himself. Would you fight for man if they stand lazy on the side expecting you to take care of things. The battle between good and evil are the torments of man, not of God.

An indirect answer to your question:

In Genesis 1 God works at creating order out of chaos. He starts the process of dividing organizing. As creation draws to a close (after much of the work is done) He gives man authority and a mandate to continue this orderly work of "subduing" a small portion of creation, namely the earth. With God as the ultimate source of man's strength, knowledge, ability, all these attributes being needed by man to further subdue, God in essence is still at work through / with the man. However, He is giving humanity the opportunity to work with Him, and thus learn and grow.

This template of God working through man repeats itself in the work of salvation, Christ doing most of the work, and we through the Spirit's help continue with the finishing touches. 1 Cor 3:9

As He has called us to participate with Him in His work, so the angels on a different plain of existence have been invited to participate as well, with the power, strength and intellect that He ultimately supplies. Col 1:16-17;20 It is not out of impotence that He needs our help or the angels cooperation, more out of desire; a desire for relationship as mirrored in Christ's desire. John 17:22-24. The opportunity to work with God brings us closer to Him, something He desires.

I'll try an LDS answer.

What is this war we are talking about?

Let's look into premortal life:

Abraham 3:22-28

22 Now the Lord had shown unto me, Abraham, the intelligences that were organized before the world was; and among all these there were many of the noble and great ones;

23 And God saw these souls that they were good, and he stood in the midst of them, and he said: These I will make my rulers; for he stood among those that were spirits, and he saw that they were good; and he said unto me: Abraham, thou art one of them; thou wast chosen before thou wast born.

24 And there stood one among them that was like unto God, and he said unto those who were with him: We will go down, for there is space there, and we will take of these materials, and we will make an earth whereon these may dwell;

25 And we will prove them herewith, to see if they will do all things whatsoever the Lord their God shall command them;

26 And they who keep their first estate shall be added upon; and they who keep not their first estate shall not have glory in the same kingdom with those who keep their first estate; and they who keep their second estate shall have glory added upon their heads for ever and ever.

27 And the Lord said: Whom shall I send? And one answered like unto the Son of Man: Here am I, send me. And another answered and said: Here am I, send me. And the Lord said: I will send the first.

28 And the second was angry, and kept not his first estate; and, at that day, many followed after him.

I guess this is not complete without also citing

Moses 4:1-3

1 And I, the Lord God, spake unto Moses, saying: That Satan, whom thou hast commanded in the name of mine Only Begotten, is the same which was from the beginning, and he came before me, saying—Behold, here am I, send me, I will be thy son, and I will redeem all mankind, that one soul shall not be lost, and surely I will do it; wherefore give me thine honor.

2 But, behold, my Beloved Son, which was my Beloved and Chosen from the beginning, said unto me—Father, thy will be done, and the glory be thine forever.

3 Wherefore, because that Satan rebelled against me, and sought to destroy the agency of man, which I, the Lord God, had given him, and also, that I should give unto him mine own power; by the power of mine Only Begotten, I caused that he should be cast down;

So, the angels were there before the conflict and the angels are us humans. Further, i will cite Gordon B. Hinckley, at that time apostle, and later president of the church:

"The War we are winning", October 1986

But there is another war that has gone on since before the world was created and which is likely to continue for a long time yet to come. John the Revelator speaks of that struggle:

“And there was war in heaven: Michael and his angels fought against the dragon; and the dragon fought and his angels,

“And prevailed not; neither was their place found any more in heaven.

“And the great dragon was cast out, that old serpent, called the Devil, and Satan, which deceiveth the whole world: he was cast out into the earth, and his angels were cast out with him” (Rev. 12:7–9).

That war, so bitter, so intense, has gone on, and it has never ceased. It is the war between truth and error, between agency and compulsion, between the followers of Christ and those who have denied Him. His enemies have used every stratagem in that conflict. They’ve indulged in lying and deceit. They’ve employed money and wealth. They’ve tricked the minds of men. They’ve murdered and destroyed and engaged in every other unholy and impure practice to thwart the work of Christ.

So,

1. The subject of this war is the alignment of its very soldiers, us
2. The only way God could possibly, by divine intervention, end this conflict, is by taking away the agency he means to protect, and force everyone to "be good" - that's contrary to his goals
3. Also, on a side note, the fact that there is this war means everyone eventually has to pick sides, as at least one side is constantly trying to influence them. This means people can choose good over evil.

God graciously allows the Angels to fight the battles with the Devil and his demons. God is omniscient and already knows who will be successful in every battle between The Arch Angel Michael and Satan and his rebellious Angels.

If God himself were to oppose Satan it would not be a battle since God is omnipotent. There are other factors which need be considered also, God does not unleash all of his Angels against them either. We know this because only one third of the Angels rebelled with Satan.

Revelation 12:4 KJV And his tail drew the third part of the stars of heaven, and did cast them to the earth: and the dragon stood before the woman which was ready to be delivered, for to devour her child as soon as it was born.

With a two to one advantage it would have been a short war.

So it seems that God is even gracious to his enemies, which may give some insight to:

Matthew 5:43 and 44 KJV have heard that it hath been said, Thou shalt love thy neighbour, and hate thine enemy. But I say unto you, Love your enemies, bless them that curse you, do good to them that hate you, and pray for them which despitefully use you, and persecute you;

and also:

Luke 10:19 Behold, I give unto you power to tread on serpents and scorpions, and over all the power of the enemy: and nothing shall by any means hurt you.

Unless I am mistaken when Jesus refers to the enemy he is referring to the Devil.