87 players have career batting averages of 1.000. By the way the math of baseball stats work, all of those players also have career on base percentages of 1.000.
The list of players with perfect career OBPs is longer, though, since there are more ways to get on base than just hits. The OBP list only has 47 more people on it. That means 47 people in major league history have reached base by means other than a base hit. That means they never recorded an official at-bat.
Two Yankees appear on the list of people who have 1.000 OBPs but no at-bats. One is Kei Igawa.
Igawa famously spent most of his five-year contract being not very good or in Triple-A. In his brief time with the Yankees he made two plate appearances in his major league career. Both came in an interleague game against the Giants on June 22, 2007. He somehow drew a two-out walk off Matt Cain in the second inning. Two innings later, he sacrifice bunted. He didn’t hit again in the majors, finishing his career with two plate appearances and zero at-bats.
The vast majority of people on the 1.000 OBP list are pitchers, which makes sense. Half of the league doesn't have them hit anymore, and even before that was true, they still got far fewer at-bats than position players. It checks out that plenty could bat once, somehow reach base, and then never bat again.
39 people on the list were position players and pinch-hitters. One other Yankee appears in this group.
Honey Barnes made his major league debut for the Yankees as a 26-year-old on April 20, 1926.
There’s not a ton about Barnes’ career before this game. He was 26, so he likely didn’t come straight out of college. There are no listed minor league stats for him on Baseball Reference before he played in the majors, but presumably he was playing somewhere. Even on his Wikipedia page, the only thing there is that he played baseball at Colgate with fellow major leaguer Eppie Barnes, and that the two seemingly weren’t related.
Somehow, he ended up with the Yankees in 1926 and was on the bench for a game against the Washington Senators on April 20th. The Yankees scored 15 runs in the first seven innings and were ahead late. In the top of the eighth, they scored another three runs to go up 18-2.
Barnes was brought in as a defensive replacement at catcher in the bottom of the inning. After the Senators scored a run in the inning, Barnes was due up first in the top of the ninth and walked. The next three batters went down in order and the inning ended.
The Senators scored two runs in the bottom of the ninth as Washington ran all over Barnes. Four different runners moved up a base during the inning, but admittedly all were scored as defensive indifference. The Yankees still ended up winning 18-5.
Just like Barnes randomly appearing on the roster, there’s no real transaction history for how he left it, but he did leave it. The game against the Senators would be his first and only major league appearance. He ended his career with one walk and zero at bats.
Barnes played at least four more seasons in the minors before disappearing off the baseball radar. It probably wasn’t the major league career he hoped for, but he is technically the all-time leader in OBP.
A third Yankee nearly made this list: Fred Holmes. He walked in his one career plate appearance in 1903 with the Highlanders before leaving the team. However, the extremely rude Cubs gave Holmes three at bats the following year, and he did not maintain the 1.000 OBP.
Having a high on base percentage is obviously a good thing. That being said, having it be 1.000 isn’t ideal for the player, because that means they didn’t play very much.
Data courtesy of the Baseball Reference Play Index