I think that the whole idea of platooning players to a lineup to have more left handed hitters against right handed pitching and vice versa is dumb. However, if so many managers believe it, why not do this. Allow your "starter" to pitch to the first batter. The lineup sheet had already been turned in to the umpire and offical scorers, so the manager is somewhat "stuck" with them. Change to another pitcher that throws from the opposite side as the original starter. The other manager can not re platoon this early or he has too little bench for later innings as pinch hitters, pinch runners, or defensive replacements. This would stop all this lefty/righty "percentage" crap.
With the stats available, a manager should check to see how any picture/ batter matchup results have fared. Some lefties tend to hit lefties well. Some right handed pitchers get left handers out as well or better than right handers. Also you can see whether this pitcher tends to get this batter out or not. This would be TRULY playing the percentages, but these managers have blindly been following old outmoded ideas for over 100 years.