Because it still takes effort to give things away for free and as a robot owner, natural resources, land, rare skills can't be automated away.

Effort is a human skill, which the premise states is already automated. As are rare skills.

If you can even automate giving things away without worrying about people hacking/stealing/vandalizing your robots, then wouldn't it also be likely for you to spend all your resources on combat robots to take resources/land from other robot owners instead of wasting them on people that aren't giving you anything you want?

Why would the elite worry about that, life is good in a monopoly, no need to upset the balance.

Because resources don't last forever? Nor are they distributed among the land equally (for example oil,rare earth elements, uranium).

Those are all current resources. The general currency is "energy" and "materials", and even materials are based on the energy in creating them (I don't think REEs are that rare, but they are hard to process).

There is no research to even suggest that we are going to be able to synthesize one type of matter to another arbitrary type without expending an absurd amount of energy, making it useless to do.

The idea that you could do something like that is even more outlandish than having robots that could automate everything a human could.

> one type of matter to another arbitrary type

But I didn't say this.

Certain materials can be substituted for another, but for high energy costs in making them.

Why would you give it away for free? Also, you're forgetting the cost of raw materials.