It's possible I just dreamed this up, but I * think I remember Captain giving a speech about the Federation in a TNG episode. It was about making a better world and improving ourselves. Similar to the shpiel he gave to Lily in First Contact, but I was thinking this one was longer. Did I just make this up? If not, can anyone throw an old school nerd a bone here? My first convention was over 20 years ago, and I got an autographed 8x10 of John de Lancie. Similar to this from First Contact: "The acquisition of wealth is no longer the driving force of our lives. We work to better ourselves and the rest of humanity. Actually, we're all like yourself and Dr. Cochrane." Thanks a bunch!
^I think that was lifted from his exchange with the stockbroker in "The Neutral Zone" (Season 1 finale).
Just found it on youtube, I believe you are correct! Unfortunately, it's not as poignant and dramatic as I had recalled. Still a great find, and you posted within literally one minute of my question. Major props, and thanks again!