This is because Fed has dual mandate and it's job is not just to promote full employment but also financial stability. In the widely used dynamic stochastic general equilibrium models, that Fed also uses according to their publications, once the output gap closes you get extra inflation.
Fed's control over economy is not that precise that they can hit exactly 0 output gap. We do not even know exactly how big output gap is at every moment in time. Macroeconomic data are published with delay, and can be revised even years after original publication. Consequently, Fed is working blind folded, they only have estimates of what the output gap is based on forecasting models which can sometimes have non-trivial forecasting errors.
In that sort of environment it makes sense that Fed will already stop monetary stimulus before they completely close the gap, because they do not know exactly where the gap is and they also worry about inflation, so just keeping their foot on the monetary pedal till the gap is obviously closed is not an option for them as that would mean that over long periods of time they consistently overshoot their inflation target.