You are quite correct. Jesus’ Kingdom is a spiritual one. My husband has stated for years that IF we Christians were adequately responding to the guidance of His Holy Spirit, people would not even look to the government for help.
I certainly agree with you that Jesus' kingdom is a spiritual one. However, I don't agree that people wouldn't look to the government if Christians were adequately responding to the guidance of the Holy Spirit. Covetousness and envy are part of the human condition, and if people see a chance to get something for nothing, they will often take it. While Christians might practice "tough love" (for example, providing necessities but not luxuries to people who can and should work for themselves but don't), it's quite natural for takers who see their productive neighbors enjoying the fruits of prosperity to want luxuries for themselves, and maybe even to want their neighbors to be deprived of them. Christians tend to be more concerned with meeting the actual needs of as many people as possible, not propping up relatively few in luxury. Also, when you're able to choose the recipients of your generosity, you tend to give to people you know, which helps you filter out fraudsters and people who are only weakened by free goodies.
It's much easier to lobby the government to force the prosperous to hand over free stuff than it is to stand on one's own feet economically and have to witness other people who, for whatever reason, have more stuff.