Below are CNC applications:
I use machine taps in tension compression holders. Functionally like rigid tapping, but with some fudge factor for machines that do not have a C-axis. Typically I run this at 500RPM, and switch to low gear in anything harder than aluminum. I have used these on blind holes, but only if I can substantially over drill the depth. If you bottom or chip pack the hole out it will break. Works best for through holes with spiral point taps.
I use single form thread mills on the high spindle speed machines. I cut from the bottom up tracing the full thread. Blind holes. Through holes. Doesn't matter. If you start at the bottom all the chips are below your cutter.
I use full form thread mills on the slower spindle speed machines. I start at the bottom and turn 1.5 to 2 thread rotations and done. Doesn't leave the chips behind as well as the single form does, but since its only making 2 interpolations at any depth (upto its flute length) chips are not a problem. I start at the bottom anyway. Works fine in blind holes or through holes.
What exactly is the advantage of a three form thread mill?
For clarity the form is the number of teeth in a single flute. There may be multiple flutes in single form, full form, and three form thread mills.
Single form can be made in house on a tool D-bit grinder with just one "flute" with one tooth. I buy multiple flute single form thread mills from Carbide Tool Source (Rogue Systems Inc) and I usually buy full form thread mills from Lake Shore Carbide. If I find a reason to try three form thread mills I'll probably start with some "cheap" Chinese imports off Ebay to see if the concept works for me or not.