With the 1 game format, it ensures that the wild card team's best pitcher won't pitch twice in a 5 game first round series, as a penalty. However, with a 3 game play-in series, this could still happen. For example, for the first round, teams will play 5 games in 6 days. The Wild card team will have to play 6 games in 7 days. So their rotation would look like:
Day 1- #1 pitcher used for play-in game
Day 2- #2 pitcher used for Game 1
Day 3- #3 pitcher used for Game 2
Day 4- travel day
Day 5- #4 pitcher used for Game 3 OR #1 pitching on short rest, possible elimination
Day 6- #1 pitcher used for Game 4 on full rest OR #2 on short rest, possible elimination
Day 7- #2 pitcher used for Game 5 on full rest OR #3 on short rest, possible elimination
Here we see the Wild Card team only gets to use their #1 once in the first round because of the penalty.
If there was a 3 game play-in, then the Wild Card plays 8 games in 9 days:
Day 1- #1 pitcher used for play-in game
Day 2- #2 pitcher used for play-in game
Day 3- #3 pitcher used for play-in game
Day 4- #4 pitcher used for Game 1
Day 5- #5 pitcher used for Game 2 OR #1 on short rest
Day 6- travel day
Day 7- #1 pitcher used for Game 3 OR #2 one short rest, possible elimination
Day 8- #2 pitcher used for Game 4 on full rest OR #3 on short rest, possible elimination
Day 9- #3 pitcher used for Game 5 on full rest OR #1 on short rest, possible elimination
This would allow the wild card team to possibly use their #1 and #2 twice in a 5 game series, albeit on short rest. Even worse, if there was a travel day in between the 3 game play-in and the first round (most likely), then the Wild Card team would only have to use their #1 once on short rest for Game 1, and then get him back in Game 5 at full strength.
A team with a great bullpen but less than stellar starting rotation, such as last year's St.L or this year's Atlanta, could essentially limit the #1's innings/pitch count on short rest and shorten the game with their bullpen. As a result, even the short rest penalty wouldn't hurt them much and teams like this could still get quality starts out of their #1 on short rest. So for the penalty to really be effective, you want that #1 only touching the ball once as a starter in the first round so it will affect all teams of different builds equally.
Also consider that a 3 game play-in would lengthen the playoff schedule, something that has already been criticized as too long by some.
Summary: I think the Wild Card team should only be allowed to use their #1 once in the first round as a penalty for not winning their division. A 3 game play in would take this away. Also, a 1 game play-in will not lengthen the playoff schedule short and prevent the playoffs from running too far into October.