This is a great thread and great advise.
I do in fact use a tap jig for all tapping jobs.
Actually I use three different tap jig/handles depending on the application.
First is my B-Square chuck mounted tap handle that I use on my drill press, this is the set up used for general purpose tapping.
The part must be fixtured to the press table, the spindle lowered to bring the tap to bear, then the tap is hand rotated while bearing down and backing off the spindle using the hand wheel.
Second is a bench mounted jig from Grizzley that I use for shallow hole tapping on flat surface applications.
Third is my Forster drill and tap jig that is used for drilling and tapping holes in receivers and barrels for sight applications. This appliance is excellent and can be used for all types of tapping from shallow small shank blind holes to heavy through holes on any rounded surface.
The Forster jig is used in conjunction with my floor drill press and the B-Square chunck mounted tapping handle.
In all three applications I still use a taper tap first.
Even though the taper tap will not actually tap a four or five thread shallow hole, It will nicely deburr the hole and make alignment and clean cutting of the plug tap a certainty.
These set-ups work well for me and I have only broken maybe five or six taps in 25 years of tapping thousands of holes. HTH