Strikeouts are a non-productive out. I'd rather see my guys putting the ball in play. Runners can advance on a ground out or a fly out. Errors or negative plays can allow a batter to reach base on a ball in play that would have otherwise been an out. None of those things happen with strikeouts.
And if we're talking about a leadoff hitter, keep this in mind . . . there's only one plate-appearance per game in which he's guaranteed to be batting with the bases empty. All other times, putting the ball in play, even for an out, has the potential to result in something more productive than a strikeout.