The short asnwer is yes, but not every story needs an end as the OP. Sure the adventures we see need a begining a middle and an end, but the overall story doesn't. The Adventure is ust begining to paraphrase one of the taglines from one of the ST movies.
In the 22nd Century we had Archer
In the 23rd Century we had Kirk
In the 24th Century we had Picard, Sisko and Janeway
What of the 25th, 26th, 27th, 28th, 29th, 30th... Centuries? There is a whole universe of possibilities to explore.