"Comfortable Pessimism" Though I don't agree with much of your characterization or the usage of non-neutral terms such as "comfortable" or "convenient", what you are discussing reminds me of Joshua Foa Dienstag's thesis in his excellent work, Pessimism: Philosophy, Ethic, Spirit which delineates the common themes and minor divergences between prominent Pessimists from Rousseau to Unamuno. Part of Dienstag's project is how Pessimism can and has been used as a foundation for political action, and while he himself doesn't provide an appellation to either categories, he nevertheless separates the Pessimists into two groups of what may be described as "Active Pessimism" vs. "Inactive Pessimism" in a strictly political sense.
For Dienstag, Active Pessimists include Leopardi, Freud and Camus, while Inactive Pessimists include Rousseau, Schopenhauer, and Cioran. I'm actually surprised that you would group Leopardi with the latter considering that Leopardi writes positively about taking action despite the unhappiness often generated by it. He uses the figure of Christopher Columbus as an exemplar of one who took action despite the risks it involved.
Given the descriptions you provide, I would have to argue that you don't exactly understand the thinking behind Pessimism. For any pessimist, the inaction of a 'Comfortable Pessimist" wouldn't lead to a self-fulfilling prophecy of human suffering because human suffering would be unavoidable regardless of any action taken. Likewise, for the "Active Pessimist", there can be no "prescription to end the problem once and for all", as that assumes a linear ending to history which betrays a foundational pillar of Pessimism. An Active Pessimist may attempt to mitigate or eradicate gratuitous forms of human suffering, but would need to acknowledge that such attempts can fail, or that such problems can always return during or after the lifetime of the Pessimist.