One reason it might be hard to believe is that governments in many cases have a direct economic incentive to assist people in maintaining long, productive lives. This is because they make their money primarily off of taxes. The more people paying taxes, the more money for the government.
If, however, they could institute a system that covertly culled the less productive elements of the society while preserving the more productive, they would be lowering costs and increasing revenue. Such a system would need to target a certain socio-economic group.
Where it becomes more complex, though, is that the more wealthy individuals are, the less they depend upon the government. The most ardent supporters of the system are those whose lives depend upon it. This is why some have likened welfare to the government buying votes. If you have a political party that's main contribution to the society is to shell out social programs for the lower classes, you then have a society which benefits from a majority of people being poor and dependent.
That's sort of the contradiction at play with those who believe in government control theories... One is that the government wants to eliminate the poor, the other is that the government wants to increase poverty as a mechanism of control. Perhaps some might say that a party on the right is using the first control strategy and the party on the left is using the second... But that ultimately both parties have in mind the same basic principle that you need to leverage one class against another in order to maintain stability and power.