You are absolutely correct about one thing though. There were many people traveling for a new life. Just like the travels from East to West in the US during the gold rush people went there for wealth, opportunity, and land but not for easy living. I suspect the push for exo planets will be the same.
If we are able to unlock FTL and the time and finacial investment to get there is low or comparable enough to a human lifetime then I see people, assuming we aren't just digital intelligence by then, moving there to start a new life and get away from whatever society is going through. There is always a disenfranchised portion of the population willing to give up their life for a new one somewhere else. Even if the journey and new life is relatively harder to what the rest of society is living in.
Course having got there they were mostly stuck without coin for passage home.
I too suspect the push to space might go similarly.