A lot of people fall for the gambler's fallacy when discussing winning streaks. It doesn't matter whether you have a winning streak of 2 or 15 games, the odds of losing a game are the same. You're not due a loss because you've been winning. Just like having 15 straight heads in a coin toss doesn't imply that tails is imminent, the streak doesn't have anything to do with the next throw of the coin.
If the argument is that a big winning streak necessitates more pressure, it's at the very least equalized by the confidence that such a streak inspires. Just compare the last two seasons by the Chiefs, when they were winning last season, they always made the right decisions in close games and won all of them. This year, the opposite is true, the more they've lost, the worst they've played and have been coached in must-win late game situations. The Pats started the year 1-2, losing to one of the worst teams in the league, beat the presumed AFC favorites, the Bills, and have played with the confidence of SB contenders ever since, and they've won every close game.
It's nothing but superstition. Losing a game to have dealt with the ''expected'' and inevitably incoming loss, doesn't, any shape or form, prevent losing the first game in the playoffs, just like going into the playoffs with a 15 win streak, doesn't increase the chances of a loss.
I'd rather the team win out, get the bye and be two home games away from the Super Bowl, rather than having to win three games against more difficult opponents, all without rest, for the same destination.