Human life spans do increase substantially (although not to 300) in the Star Trek universe. From Memory Alpha:

The average Human life span had gradually increased during their history. The average life spans during the 22nd century was about one hundred years. (ENT: “Observer Effect”) This average age was still roughly the same during the 2250, but had risen to 120 by the mid-24th century. (citation needed • edit) However, at some point in history the average life span for Humans was only 35, and by 1999 it had become higher than a millennium earlier. (ENT: “Similitude”; VOY: “11:59”) Leonard McCoy had by 2364 reached the age of 137. (TNG: “Encounter at Farpoint”)