Goalie and it's not even close. A bad performance means you just lost the game. Any other player can afford a bad day and teammates could still pick up the slack.
Also the most obvious position when it comes to stealing a game. Don't allow any = can't lose.
I think there are two ways to look at it though. On one end, a goalie is clearly the mot influential position on a game-to-game basis. They can single-handedly steal or lose games for a team.
The issue is that "elite goaltending" doesn't really exist anymore. We just watched a career back-up in Korpisalo be the biggest reason for taking down one of the best offenses in the league. The guy 2 seasons removed from winning the Vezina (Rinne), never got a chance to sniff the crease in the play-ins this year despite the much more inexperienced Saros playing poorly in front of him. The guy a lot of people consider the best goalie still (Price) has been dead-on average for save % the last 3 seasons at .910, with 2 of those 3 seasons being below the league average.
It's very random year-to-year, there's very little consistency. When you're talking about elite goaltending, I don't really think there's a big difference between that and the league average "replacement level player" at the NHL level.