I’ve never heard that the impeachment hurt Gore. In fact, what I always hear is that Gore running away from Clinton backfired.
And why did he run away from Clinton to begin with? Rhymes with lin-deechment.
Actually it rhymes with "had an affair with a White House shmintern". At most, one could argue that impeachment raised the salience of the issue.
The 2000 election was close enough that you could make the case for a hundred different things making the difference between a Gore win and a Gore loss. Nonetheless, I think the narrative about impeachment costing Gore a win lacks strong supporting evidence. It seemed to emerge largely because people wanted to make the point that impeaching Trump would actually benefit Democrats politically (and they seem to have been wrong there, given that Trump's approvals are currently the highest they've been since his first year in office).
What is clear to me, though, is that the drive to impeachment cost Republicans in the 1998 mid-terms, leaving Bush with narrow majorities to push his programs through Congress.
And then Trump lost by more than Romney! His opponent taking a larger vote share than Reagan himself. Hmmm.
Trump lost the national popular vote by more than Romney, but the national popular vote doesn't determine the winner of a presidential election. Similarly, Biden winning a larger share of the popular vote than Reagan in 1980 does not have any direct bearing on the outcome of the elections each ran in, especially considering that 1980 saw a relatively strong third party candidate. Trump lost the tipping point state by less than 1 point, whereas Romney lost it by about 5 points and Carter lost it by about 8 points, and those margins do a much better job of describing how close each election actually was.