I hope you're right but I think it won't be pretty in all cases. It's easy to forget the industrial revolution wasn't entirely positive for common people or for that matter the environment.
The closest stars are way too far to reach on any reasonable timescale. That's not even mentioning the fact that moving forwards is a vague goal. Moving forwards towards what exactly? And if the US government got off of it's ass to... Oh I don't know, maybe fix the bullshit healthcare system we have and help people with tax money instead of bombing people for Israel things would improve quite a bit in a very short time. That's assuming we don't bomb each other over terroritorial squabbles first. In any case I don't really understand your defeatism when it comes to inequality but when it's something as difficult as interstellar space travel you seem to be optimistic.
What about the workers that will be eventually replaced by said robots? You think they're just going to get free money to exist? Most likely they'll end up in the private prison system or in institutions while the corporations pocket all of the savings. Things are a lot more complicated than they seem I think...