As Samuel aged and his sons were corrupt leaders, the demand might have some practical application as the people saw the way things were headed but instead of trusting God's setting them apart, making them special, they looked around and wanted the thing everyone else had....A king.
Instead of appreciating their uniqueness, they saw themselves as weird. The Lord's response is also different than you would expect. Time and time again, the Lord does not give into the demands of the people to be like everyone else and provides for them a path to take that is for their best interest. The Lord does not listen to Abraham and Moses bargaining and remains steadfast even when it comes to destruction. The Lord does not allow Moses and Aaron to return to Egypt so that God's people might die there. The Lord does not allow a lot of what the people want because the Lord knows better. But here, The Lord allows the people to get what they want. "Give them what they ask for. They are not rejecting you (Samuel) but they are rejecting me as their king."
{Foreshadowing a little here but 3 out of 40 kings do what is right in the eyes of the Lord. This does not go well for the people.}
The people will get what they want...a king. But there will be more corruption, more greed. But there is an important shift that does take place here. The king will now be the Lord's representative here on earth. Yikes!
Lord, forgive us when we forget to acknowledge that you know what is better for us than we do.