I’m with you in your opinion that government shouldn’t try to give people purpose but I think the last part of your argument is an overreach.
You’re conflating purpose with making money. They’re not the same. Counterexample: Vincent van Gogh. His purpose was clearly art but he did not see professional success while alive. If you don’t consider Van Gogh’s purpose to be something like painting or art then I’d suggest you’re not using the word as it is commonly defined.
Also I’d suggest that it’s unfair to paint the poor broadly as not seeking purpose and instead searching for temporary pleasures. I have simultaneously known both an economically struggling person who refrains from drugs and alcohol and a well-to-do person who is a functional alcoholic.
Certainly alcoholism can make people lose money, relationships, etc. But it does not follow that simply abstaining from these things will make one wealthy.