Why was the nation of Israel punished for the sin of Achan?

The story of Achan (Joshua 7) is a great, if harsh, example of community, and communal responsibility. God always considered Israel as a corporate unit in a covenant relationship with Him. His commands were to the nation; His desire for relationship with them was expressed as a national outcome. His desire for impacting the world with Him was dependent on a people living totally separate from the world, and totally committed to Him. For that reason, God’s desire for that Israel be His possession as a nation, sin was dealt with in a corporate way, so many did suffer, even if the failure was a single individual. But it worked in a positive way too, when God’s love and mercy was on display. When once a year the high priest entered the Holy of Holies on the Day of Atonement (Yom Kippur), that atonement was for the sins of the entire nation. If atonement impacted all, then certainly sin was viewed the same way.
In the story of the conquest of Jericho, Joshua had specifically commanded, The city and all that is in it are to be devoted to the Lord. Only Rahab the prostitute and all who are with her in her house shall be spared, because she hid the spies we sent. But keep away from the devoted things, so that you will not bring about your own destruction by taking any of them. Otherwise you will make the camp of Israel liable to destruction and bring trouble on it. All the silver and gold and the articles of bronze and iron are sacred to the Lord and must go into his treasury”—Joshua 6:17-19. Jericho was going to be the first city conquered in the Promised Land. Throughout their journey with God, the Israelites had always been commanded to give the first of anything—their children, their crops, whatever—to the Lord. So all of Jericho being “devoted to the Lord” was not a new idea with the context of their history. Beyond that, of course, Joshua had made the parameters of this conquest incredibly clear—and still Achan disobeyed. Because Israel was seen as a single entity, this was a national sin. It was an important issue because God did not want Israel contaminated with the peoples and practices of the land in which they were coming. Plundering some of these items would be a reminder of those practices—practices for which they were being completely destroyed. God wanted Israel to remain pure. Beyond that of course was the willful disobedience that Achan so easily exhibited. Centuries later, Jesus would say to His disciples, If you love me, you will obey what I command—Jesus Christ, John 14:15. That was nothing new but simply God in the person of His Son saying what He had said from the beginning, going all the way to the second commandment: You shall not make for yourself an idol in the form of anything in heaven above or on the earth beneath or in the waters below. You shall not bow down to them or worship them; for I, the Lord your God, am a jealous God, punishing the children for the sin of the fathers to the third and fourth generation of those who hate me, but showing love to a thousand generations of those who love me and keep my commandments—God speaking, Exodus 20:4-6. That same idea was shared by Moses to the people just prior to their entering into the long-awaited Promised Land: See, I set before you today life and prosperity, death and destruction. For I command you today to love the Lord your God, to walk in his ways, and to keep his commands, decrees and laws; then you will live and increase, and the Lord your God will bless you in the land you are entering to possess. But if your heart turns away and you are not obedient, and if you are drawn away to bow down to other gods and worship them, I declare to you this day that you will certainly be destroyed. You will not live long in the land you are crossing the Jordan to enter and possess. This day I call heaven and earth as witnesses against you that I have set before you life and death, blessings and curses. Now choose life, so that you and your children may live and that you may love the Lord your God, listen to his voice, and hold fast to him. For the Lord is your life, and he will give you many years in the land he swore to give to your fathers, Abraham, Isaac and Jacob—Deuteronomy 30:15-20. And imagine what might have occurred if, following God’s command and the discovery that someone had indeed disobeyed, nothing had happened. God needed the nation to see that sin, disobedience, disregarding His word, had incredibly serious consequences. God doesn’t want us obedient some of the time—like when it’s convenient or when we understand His motives. He wants us obedient all the time. His standards haven’t changed.
Incidentally we see the many suffering for the one all the time, especially in sports. We may single out one “goat” for losing a game but, in the record books, the whole team lost.