Okay, I thought y'all be smart enough to pick up and talk about my point, but apparently I need to explain it.
My point is when does the pitcher stop becoming a fielder and return to the status of a pitcher?
Based on what I am reading in the replies, the pitcher is always a pitcher and never a fielder. Do you enforce the LBR immediately if a pitcher catches a ball in flight in the circle? If so, you have removed a runner's right to tag up and advance on a caught fly ball. Of if running on the pitch and has reached the next base, the ability to attempt to return to the base they need to tag to avoid being put out.
This was discussed two years ago at the UIC Clinic with Walt Sparks and, at least in my group, the consensus seemed to be that the LBR isn't in effect until, in the judgment of the umpire, the effects of the ball being put into play are completed.
Think about it from a runner's point of view. A throw from the outfield is cut off by SOMEONE in the middle of the infield. Do you really expect the runners and coaches to be able to immediately identify this player as the one who pitched the ball and adjust their running assignments accordingly?
As previously stated, I don't believe this was the purpose of the LBR. Whether I like the rule or not is irrelevant to the discussion.