The problem is that that base of support may not comprise a majority of voters. We don’t want to elect someone whose base is narrow but fervent, who’s deeply disliked by a majority of voters, and who wins only because there are too many other candidates in the race splitting the vote with one another. (If you’re talking to Democrats feel free to hint that this came to pass in the 2016 Republican presidential primary.) Yes, under plurality the candidate who turns out the biggest base is the one who wins; but perhaps another candidate would have an even bigger base had a “spoiler” candidate chosen not to run.

To note when answering this question: be careful not to make it seem as though having more people vote is a detriment.