Fling administration clerk sounds like somebody you let a computer do and a society can work despite of some people who do not work. Capitalism has functioned for two centuries and if you take a look at long run employment stats full employment has been the exception (during the social democratic era). All the people we see in Trek work because they love their jobs. Some of them like the chief engineers even regularly work over hours. And there is nothing glamorous about fixing a broken piece of machinery or crawling through some Jeffries tubes, it is hard work.
Happiness studies have suggested that being unemployed causes more loss of well-being to people than the mere loss of income could explain so we have firm empirical evidence which suggests that the economic ideas of Trek are not at all unrealistic.