Some recent theoretical studies tended to employ analytically-continuous gaussian, or infinite-bandwidth step pulses to examine tunneling process. The stationary phase method is often employed to this aim. However, gaussian functions do not have a well-defined front, such that their speed of propagation becomes ambiguous. Also, infinite bandwidth signals cannot propagate through any real physical medium (whose transfer function is therefore finite) without pulse distortion, which also leads to ambiguities in determining propagation velocity during the tunneling process. In this manuscript, we appoint some incompatibilities with the application of the method of stationary phase in deriving tunneling times which, eventually, can ruin the superluminal interpretation of transition times.1918883888