"Like all the other nations..." Why would the Jews want a King?

(4) Then all the elders of Israel gathered themselves together, and came to Samuel unto Ramah. (5) And they said unto him: ‘Behold, thou art old, and thy sons walk not in thy ways; now make us a king to judge us like all the nations.’ (6) But the thing displeased Samuel, when they said: ‘Give us a king to judge us.’ And Samuel prayed unto the LORD. (7) And the LORD said unto Samuel: ‘Hearken unto the voice of the people in all that they say unto thee; for they have not rejected thee, but they have rejected Me, that I should not be king over them. (8) According to all the works which they have done since the day that I brought them up out of Egypt even unto this day, in that they have forsaken Me, and served other gods, so do they also unto thee. (9) Now therefore hearken unto their voice; howbeit thou shalt earnestly forewarn them, and shalt declare unto them the manner of the king that shall reign over them.’ (10) And Samuel told all the words of the LORD unto the people that asked of him a king. (11) And he said: ‘This will be the manner of the king that shall reign over you: he will take your sons, and appoint them unto him, for his chariots, and to be his horsemen; and they shall run before his chariots. (12) And he will appoint them unto him for captains of thousands, and captains of fifties; and to plow his ground, and to reap his harvest, and to make his instruments of war, and the instruments of his chariots. (13) And he will take your daughters to be perfumers, and to be cooks, and to be bakers. (14) And he will take your fields, and your vineyards, and your oliveyards, even the best of them, and give them to his servants. (15) And he will take the tenth of your seed, and of your vineyards, and give to his officers, and to his servants. (16) And he will take your men-servants, and your maid-servants, and your goodliest young men, and your asses, and put them to his work. (17) He will take the tenth of your flocks; and ye shall be his servants. (18) And ye shall cry out in that day because of your king whom ye shall have chosen you; and the LORD will not answer you in that day.’

(14) When thou art come unto the land which the LORD thy God giveth thee, and shalt possess it, and shalt dwell therein; and shalt say: ‘I will set a king over me, like all the nations that are round about me’; (15) thou shalt in any wise set him king over thee, whom the LORD thy God shall choose; one from among thy brethren shalt thou set king over thee; thou mayest not put a foreigner over thee, who is not thy brother. (16) Only he shall not multiply horses to himself, nor cause the people to return to Egypt, to the end that he should multiply horses; forasmuch as the LORD hath said unto you: ‘Ye shall henceforth return no more that way.’ (17) Neither shall he multiply wives to himself, that his heart turn not away; neither shall he greatly multiply to himself silver and gold. (18) And it shall be, when he sitteth upon the throne of his kingdom, that he shall write him a copy of this law in a book, out of that which is before the priests the Levites. (19) And it shall be with him, and he shall read therein all the days of his life; that he may learn to fear the LORD his God, to keep all the words of this law and these statutes, to do them; (20) that his heart be not lifted up above his brethren, and that he turn not aside from the commandment, to the right hand, or to the left; to the end that he may prolong his days in his kingdom, he and his children, in the midst of Israel.

No, the Parshah was said only in order to make the people fear the king.... R' Yehudah said: Israel were were commanded to fulfill three commandments after entering the Land: to appoint a king, to exterminate Amalek, and to Build the Beit Hamikdash. R' Nehurai says, they were not commanded to appoint a king. Rather the Parshah describes the laws of kings in case they will reqeust one. As it is written (Deut. 17:14) "And you will say, 'I will set a king over myself'" etc. Rabbi Eliezer says in a Breita, The elders of Samuel's generation properly requested a king saying (I Samuel, 8:6) "Place a king over us..." but the Am Haaretz improperly requested a king saying saying (I Samuel 8:20) "And we will be like all the other nations; our king will judge us, and go forth and fight our wars."

It was taught: R’ Yosi says ‘Three commandments were given to Israel when they entered the land; [i] to appoint a king; [ii] to destroy the seed of Amalek; [iii] and to build themselves the Chosen House (the Temple) and I do not know which of them comes first. When it is said “The hand upon the throne of the Lord, the Lord will have war with Amalek from generation to generation,” (Shemot 17:16) we learn that the appointing of a king comes first, because ‘throne’ indicates a king, as it is written “Then Shlomo sat on the throne of the Lord to rule.” (Divre HaYamim I 24:23)