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What about services? Robotics can't do everything

Certainly there would still be service jobs, but capitalism itself would eliminate many of them, and convert the rest to unpaid positions done by people who enjoy the jobs. Before you write that off as perposterous, hear me out: MANY people, including myself, like to work and would continue working even if they didn't have to simply out of ethics. These people, freed from the production sectors of the economy by their eradication, would flood the service sector and drive its wages through the floor...and eventually to extinction. In a world where there is unlimited food and housing, I doubt most people would even care about this loss (what would you need money for if nearly everything is free?). The only people who would work are those who WANT to work simply to be doing something, so money wouldn't be their biggest concern anyway.

Robotics can take care of the jobs that nobody wants.

I do concur on the energy thing though. We know that the ST universe generates its energy in antimatter based reactors, but they never have described in detail exactly how they're supposed to work (eg. does the dilithium generate the antimatter, or does it simply react with it?)

If I remember correctly, only Dilithium/Trilithium and Latinum cannot be systhesized...hence the extreme value given to their mining operations by the various species in the different shows.