The purpose of the "dead cut" magneto check after start is two fold in the sense that when selecting an individual magneto there should a) be some drop but b) the engine does not stop.
a) confirms that you do not have a live mag
b) confirms that you do not have a completely dead mag!
In the case of a) - ie in the event of ZERO drop - one might then troubleshoot further by closing the throttle completely and turn the magneto switch to OFF to see what happens. If a mag is live then the engine would continue to operate in which case maintenance action would be required since it would not be possible to switch off the mags completely in the event of an emergency which requires a shutdown in the air and also the engine is live should anyone be imprudent enough to pull the propellor through whilst on the ground.
In the case of b) if you have a completely dead mag there is no point in going any further unless you are prepared to risk your neck flying around on one mag!
All these points should have been covered in basic flying training but as an instructor it is not infrequent to discover that some pilots are a little unsure as to WHY these checks are conducted as they are.
Finally, the magneto system is NOT fail safe in the sense that when you switch a mag off you are MAKING a circuit (ie grounding the mag to the engine etc.) This is yet another reason for treating a propellor as live at all times. I recently watched with horror as a private owner pulled the prop through whilst the aircraft was in the hangar!!
Hope this helps