Let me throw in my $.02 worth. Do you only own one gun and one action type? Do you ever think you might need to shoot something other than the one gun you do own?
That is the primary reason to practice "Tap (hit the magazine base to ensure it is firmly seated in the weapon), Rack/Flip (rack the slide while flipping the gun to the side to ensure the round is ejected. Also the drill for a type 2 malfunction), and evaluate, then Bang if necessary.
You can only do the "second strike" if you have a DA auto. Obviously, it doesn't work for any of the single action, Glocks or even a few makes of DA guns. If you practice a common drill, you can use it effectively with all makes.
As for pressing the trigger for a 2nd strike while reaching for the slide, what do you hope to do? Your support hand is no longer supporting. I seriously doubt that you have a sight picture or sight alignment so where is that round going to go, assuming it goes off at all? If it doesn't go off, what happened to the "Tap" part of the drill? If it does go off (big surprise, no hit on your opponent, greater muzzle flip because your support hand is not in contact with the firing hand), you can expect an even slower followup shot as you re-aquire a grip.
If you practice the T/R/F and evaluate response to a misfire (Type 1 malfunction), you can complete it in less time than it takes to say "Tap, Rack, Flip". Less than a second. I'd certainly consider that preferable to maybe getting the round to fire with a second trigger pull, and then have to T/R/F anyway.
Just to end, I say T/R/F because you really don't want firing the weapon to be a programmed response. What if your opponent dropped his weapon and was no longer a threat? You just executed him and could be charged with murder. What if your opponent was no longer visible and your programmed shot nailed a bystander, etc? Same thing. Malfunction clearances should be programmed responses that are practiced and drilled till they are reflexive acts, but the actual act of firing should always be a conscious decision.