This would allow the path to converge more quickly, as it is often the case that the climbing image is the first to converge. This would especially be useful when only the saddle point is of interest.
This should, however, not be the default behaviour, as it can regularly happen that the climbing image has converged, but the path still significantly changes over time and the force on the climbing image at some point starts to increase again, finally converging it so something else.
This would allow the path to converge more quickly, as it is often the case that the climbing image is the first to converge. This would especially be useful when only the saddle point is of interest.
This should, however, not be the default behaviour, as it can regularly happen that the climbing image has converged, but the path still significantly changes over time and the force on the climbing image at some point starts to increase again, finally converging it so something else.