Unless you've time traveled back from the year 3000, your estimates of the capabilities of robots is WAY too high.
My estimate of robot capability is based on what could be achieved if we spent a fraction of what it would cost to send a human.
Did we send a robot up to repair the Hubble space telescope?
Would we send a robot NOW, rather than a human? Probably.
In a general problem solving situation they cannot hope to match the flexibility of a person,( and remote tele-operation does not solve this). Now granted, that's using today's technology - but I would argue that developing tech. to send a human to mars will be realised MUCH sooner than tech. to develop a robot capable of matching a human/s dexterity, thinking etc.
Generally speaking, humans need to solve more problems because the systems need to sustain them tend to be far more complex than the systems need to sustain a machine. How many problems does a hammer need to solve - just the one. It doesn't ever have problems with it's life support, or running ut of food, or getting bored.
Nope - people are inherently fragile - in body and mind.
Did the Europeans colonising America have "no objective value"?
The Americas were already colonised - so over all, a net zero value.