Wealth? Isn't that just capital? Just like the infinite automated production would be capital as well.
I would rephraze this as what need is there for markets and money?
It's not about personal gain. It'd about how to manage the resource pools of an entire civilaztion.
What you are describing is the perfectly planned economy. From empirical experience national economies cannot be efficiently planned. USSR did not have the computational capability we have now - but we don't know is there any way to control a national - lest a planetary or solar economy by any other means than markets.
So, the question to me is - if solar ecomony can be planned then there is no need for markets and money, but if it's computationally intractable, or, the market way of organization is the cheapest and best way to do it, then we are stuck with markets and money up to the heat death of the universe.
Interestingly, if from algorithmic point of view markets and money is the best way to organize a civilizations resources, then it's likely alien civilizations (if they exist) will have a market economy too.
I would hope the question of reaource allocation is tractable and that the future of mankind is more like Iain Banks's Culture rather than "robber barons of the Oort cloud".