The vending machine replicator can only replicate a limited amount of items (no guns or anything else with moving parts. No game meat. Etc.)
If farming and mining are rendered obsolete, then those people can do other things, like 'service' jobs. Most of the economy in the real, industrialized world is service anyway. The US economy is 80% service.
In order to create the Sierra Madre chips you need fission batteries (for some reason) which are a limited commodity anyway, so it isn't infinite.
People would find other things to do...like become waiters, singers, soldiers, secretaries, doctors, lawyers, computer engineers, janitors, nurses, deliverymen, couriers, bureaucrats, ditch-diggers, photographers, policemen, etc., ad infinitum.
This is me, agreeing entirely.
Sorry, Enclave, but the message here is not about "screw the little guy"...it's that progress is going to happen, regardless.
The farmers and miners you talk about might be inconvenienced by the invention of a "magical replicator" but to imply that they are ruined is to say that they are not capable of learning something new, or adapting to the changing times. The argument you are making is like complaining because a candle-maker is put out of a job by the invention of the light bulb.
As for Sinclair becoming wealthy, so what? If the post-apocalypse teaches us anything, it's that nothing lasts forever. Let Sinclair have his billions...did he not earn them by coming up with something amazing that people would pay for? Why should he not profit from good business sense?
Besides: the bombs came, and everything Sinclair worked for was put to the torch, metaphorically speaking. If it hadn't been the war, something else would have destroyed him...a car accident, cancer, a brilliant scientist with an even better idea. Whatever. The point is, everything changes...except war, of course. ^_^