Push the casualty rate high enough across the whole run of the series and you end up with an extinct humanity at the end of it. Especially since there is very little evidence to suggest that humanity has any really significant colonies anywhere, and quite a bit of evidence against it. (There's also evidence that none of the other major species do either, which combined with the way the Enterprise in all its incarnations is always the only ship in the sector strongly suggests a Federation and equal-powered foes that are a great deal less wealthy that it may appear at first.) Again we run up against the writers not really seriously thinking through the consequences of their own attempts to create drama, which wrecks up attempts to take it seriously. However, "Federation as declining dystopian human empire" is certainly one popular fanon interpretation.
> there is very little evidence to suggest that humanity has any really significant colonies anywhere, and quite a bit of evidence against it
It is kind of suspicious that most of the characters are from Earth; Tasha Yar is from a colony but there aren't any other major examples.
> combined with the way the Enterprise in all its incarnations is always the only ship in the sector
Space is big, and sparse. There are apparently hundreds of planets in the Federation (explicitly stated at times). There are also hundreds of starbases. And while in the original series there are only about a dozen ships in the same class as the Enterprise, by the time DS9 rolls around we see huge fleets of hundreds of ships on screen.
