"Imagine ... we live in a world where people no longer have to work. Machines do everything we don't want to do."

In many ways, we have been living in this world for over a century. An example: https://blog.strom.com/wp/?p=7791 https://www.thehenryford.org/collections-and-research/digital-collections/artifact/141576

Hazlitt discussed machines in Chapter 7 of Economics in One Lesson. https://leeconomics.com/Literature/Henry%20Hazlitt%20Economics%20in%20One%20Lesson.pdf#%5B%7B%22num%22%3A143%2C%22gen%22%3A0%7D%2C%7B%22name%22%3A%22Fit%22%7D%5D

Each person's time is still scarce. The machines are scarce and their time is scarce. The raw materials are scarce. So they will still be economized even if we have an abundance available compared to now.

As for "inflation ... goes to those who put in the physical effort. ... are you happy with 2% inflation?" I don't think the answer to that is impacted much by the scenario. The question boils down to "is 2% theft OK?" or rather "is inflation theft in a proof-of-work scenario?" If the situation is more like US dollars, where only a few are eligible to inflate by official capacity but everyone else is banned, then no, it's not OK. If the situation is more like gold, where anybody can buy property and mine if they put in the effort, then yes, it's OK.

In your scenario something went wrong with a fixed 2% inflation that everyone is subject to. First, why should everyone be subject to this one medium of exchange exclusively? They should be able to choose among media. Second, how could it be fixed at 2% or why 2%? How can you bootstrap such an agreement? Surely one asset could be created with that 2% inflation rate, but that leads back to the first point: no one should have to use it.

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