According to Protestant interpretations why does God want people to serve Him when He doesn’t need it?

We do not serve God because He needs it but because we need it. Servants is what we are. It is what we were created to be and what sin has destroyed in us:

And why call ye me, Lord, Lord, and do not the things which I say? - Luke 6:46

God created man, put him in the garden to dress it and keep it, gave him both provision and prohibition as sustenance, established his dominion over beast and bird, and created a counterpart specifically for his benefit. All this God called good and very good.

The temptation came to determine good and evil for himself, man swallowed it, and humanity was ruined. Our disposition became to serve ourselves rather than God, to serve anything else other than God:

Who changed the truth of God into a lie, and worshipped and served the creature more than the Creator, who is blessed for ever. Amen. - Romans 1:25

Notice that even in ruin we still serve. Our created purpose has not changed: We are servants and we cannot but serve. Enmity towards God has not cancelled our servitude but it has redirected it toward ruin. We serve all the wrong things. The only service that is actually beneficial for us, though, is service to the creator. He it is that made us servants and He it is that fulfills our servitude.

"Nor is He worshiped with men’s hands, as though He needed anything". This is spoken against religion, against man's briberous appeas*m*nt of deity which is nothing more than self-servitude robed in piety. True religion is service to God through service of neighbor not sacramentalism or imposed tradition:

Pure religion and undefiled before God and the Father is this, To visit the fatherless and widows in their affliction, and to keep himself unspotted from the world. - James 1:27

If a man say, I love God, and hateth his brother, he is a liar: for he that loveth not his brother whom he hath seen, how can he love God whom he hath not seen? - 1 John 4:20

When the description comes of God's only begotten becoming one of us we have the same language:

Who, being in the form of God, thought it not robbery to be equal with God: But made himself of no reputation, and took upon him the form of a servant, and was made in the likeness of men: And being found in fashion as a man, he humbled himself, and became obedient unto death, even the death of the cross. - Philippians 2:6-8

The Son of God left his primary estate and was made flesh ... human flesh. He was made in the likeness of men. That is to say, He took upon himself the form of a servant. Humanity and servitude are synonymous in the economy of creation and when the Savior came, He came thus. To become a man he had to become a servant for that is what man is. To be a righteous man He served God.

"That all peoples, nations, and languages should serve Him" is not an addition to our estate it is a return. It is a correction of what went wrong. It is not a burden it is a blessing. It is life and fullness of joy to confess Jesus as Lord.

But you're gonna have to serve somebody, yes indeed You're gonna have to serve somebody Well, it may be the devil or it may be the Lord But you're gonna have to serve somebody - Bob Dylan "Gotta Serve Somebody"

The question (said to be in the mouth of an atheist) lacks heart.

We love him (and thus only do we serve him) because he first loved us. [1 John 4:19.]

The question is, in reality, a refusal to serve God on the grounds that he (supposedly) does not 'need' service. But that is a servile attitude, not the response of a freeborn son, who loves the Father. Parables abound which demonstrate these opposite attitudes.

Since a Protestant response is invited, I am quoting Martin Luther.

Extract from 'The Great Fire of the Love of God for us'

Taken from Martin Luther, “A Brief Instruction on What to Look for and Expect in the Gospels (1521),” in Luther’s Works, Vol. 35: Word and Sacrament I, ed. Jaroslav Jan Pelikan, Hilton C. Oswald, and Helmut T. Lehmann, vol. 35 (Philadelphia: Fortress Press, 1999), 119-120.

“The chief article and foundation of the gospel is that before you take Christ as an example, you accept and recognize Him as a gift, as a present that God has given you and that is your own.

This means that when you see or hear of Christ doing or suffering something, you do not doubt that Christ Himself, with His deeds and suffering, belongs to you. On this you may depend as surely as if you had done it yourself; indeed as if you were Christ Himself.

See, this is what it means to have a proper grasp of the gospel, that is, of the overwhelming goodness of God, which neither prophet, nor apostle, nor angel was ever able fully to express, and which no heart could adequately fathom or marvel at.

This is the great fire of the love of God for us, whereby the heart and conscience become happy, secure, and content. This is what preaching the Christian faith means.

This is why such preaching is called gospel, which in German means a joyful, good, and comforting ‘message’; and this is why the apostles are called the ‘twelve messengers.’

Concerning this Isaiah 9:6 says, ‘To us a child is born, to us a son is given.’ If He is given to us, then He must be ours; and so we must also receive him as belonging to us.

And Romans 8:32, ‘How should God not give us all things with His Son?’ See, when you lay hold of Christ as a gift which is given you for your very own and have no doubt about it, you are a Christian.

Faith redeems you from sin, death, and hell and enables you to overcome all things. O no one can speak enough about this! It is a pity that this kind of preaching has been silenced in the world.

Now when you have Christ as the foundation and chief blessing of your salvation, then the other part follows: that you take Him as your example, giving yourself in service to your neighbor just as you see that Christ has given Himself for you.

See, there faith and love move forward, God’s commandment is fulfilled, and a person is happy and fearless to do and to suffer all things. Therefore make note of this, that Christ as a gift nourishes your faith and makes you a Christian. But Christ as an example exercises your works.

These do not make you a Christian. Actually they come forth from you because you have already been made a Christian. As widely as a gift differs from an example, so widely does faith differ from works, for faith possesses nothing of its own, only the deeds and life of Christ.

Works have something of your own in them, yet they should not belong to you but to your neighbor. So you see that the gospel is really not a book of laws and commandments which requires deeds of us, but a book of divine promises in which God promises, offers, and gives us all His possessions and benefits in Christ.”