Startrek has huge resources, but not infinite. We (in western Europe and north America) reached a point of sufficient resources around 1970. Yet we still have homeless starving on our streets while the 1% who own 90% of the resources cruise around in their super yachts. If we continue this broken system then by the 24th century a typical 1%er might own 30 planets, a fleet of starships and a dilithium crystal mine, but I don't see why he would be anymore willing to share this hoarded wealth with the rest of humanity than the 1%ers of today are.
Indeed, the political resistance to welfare systems in the USA has always saddened me. It seems to me that at a certain point, a post-industrial first-world country has exactly two ways to continue its ascendance and raise the quality of life for its citizens: You can expand in an imperialist fashion (see: Britain in the 19th century, USA in the early 20th century, Germany in the late 1930's in dramatic fashion). Or you can become a welfare state (see: Germany post-WWII, Sweden, France).
The USA has a cultural heritage of expansionism. In the 1850's, losing everything was no biggie, you just moved to California and started digging. In the 1940's, losing everything was no biggie, you just joined the army and shipped out for the Philippines. But by the 1960's when imperialism more or less became untenable (see: the entirety of Africa), there were no more safety nets. America continued in its headstrong belief that no man needs charity, that hard work will provide opportunities for anyone who looks.
The rich always want to be richer. There's two things to do when a first-world country exhausts its own easily-exploitable resources: acquire more resources by force, or redistribute wealth. Otherwise the rich will exploit the only remaining source of wealth which is a country's middle-class.
