Computers are far superior at monitoring parameters than humans. A five second check by a crewmember during taxi is next to useless if you consider that the computer monitors the system from the moment that gyros erect until shutdown. Computed comparisons also check minute discrepancies that may go unnoticed in poor light or during the many distractions enroute to the holding point.
EFIS systems also come with a test button that self-tests some fifteen or so parameters, much like the POST conducted when you switch on your desktop computer! The purpose of such systems is to permit crews to spend more time on other vital actions. Besides if you folk consider the multitude of components that make up an EFIS generated display, including inputs from air data computers, navigation aids, transducers, AC and DC power sources, internal electrical components and circuits, you could spend an hour checking the authenticity of the indications and still not arrive at a positive conclusion.
A check of the standby/emergency system is important and this may be done by visually comparing the information presented to that displayed by the primary system.
I know that it is hard to change from old habits but such a test as turn right, skid left, wings level, numbers increasing does not scratch the surface of EFIS generated information.