FWIW the holes in Jim's pictures using the single drills are not typical. Usually the bits are 1" like the ones in the video. Depending on the weather, healing time with the 1" bits is not much longer than an aggressive core aeration.
The benefits of the drill and fill is it can go deeper than other methods and since it uses a drill bit, it completely removes the old material leaving a clean column which is then filled with sand. This prevents contamination from the old material.
Two courses where I previously worked did the procedure. One was relatively new but an incorrect greens mix was used which resulted in them not draining. The drill and fill was used to bore channels to the gravel drainage layer underneath which greatly helped move water. The greens were really bad (as was the climate) and the conversion rate was too slow so they ultimately rebuilt.
The other course was old, built on sand with push up greens. We found that about 12" down there was an ash (of some other type of hard pan layer) that was preventing them drain. Since every green had it we assumed that they were built that way so they would hold water, in the days before irrigation. The drill and fill provided a method to break through the hard layer into the sand below and greatly increased drainage.
In these two scenarios there was a free draining layer below so the water could easily get away. In other cases, not lucky enough to have a free draining layer underneath, the drill and fill will extend the depth of the "bucket". The more channels, the bigger the bucket and in time, with multiple drill and fills, the greens profile will slowly convert from the native soil to a sandier one. Adding XGD/TDI (or similar) drainage helps get the water drain from the 'bucket'. As the profile composition changes from the drill and fill, it will facilitate getting water to those drains quicker.
As mentioned I wouldn't be concerned about the amount of times it's used as the more channels there are the better the drainage will be.