Getting a win under your belt at the start of an event may be important in more ways than one. For me, getting off zero is my primary consideration in any event, before I set my sights on further goals (reaching 50%, winning the tournament, scoring that elusive GM norm etc). At the higher levels of chess, it may be important for another reason.
After he won the World Championship in 1960, Mikhail Tal wrote a very detailed book on the match. In this match, against Mikhail Botvinnik, he got off to the very best of starts, by winning game 1. In his comments about the game, he pointed out that the victory had one important effect. As defending champion, Botvinnik only needed to draw the match, and therefore would be happy if all 24 games were drawn. Once Tal had won the first game, this equation went out the window, and as a consequence Botvinnik was now forced to play for a win, at least in some games. This meant that Tal could prepare for a slightly 'different' opponent, at least until the match returned to even terms.
Of course this assumes that Botvinnik was willing to employ a 'drawing' strategy in the first place. It may have been the case that he did not, and that the opponent Tal now faced had not changed in any way. But I cannot help but be reminded of the recent Candidates matches, where drawing strategies were certainly on show. And I wonder if those that went down in the playoffs should have tried to negate this strategy by throwing all their energy into the first game, rather than conserve it for the last.