Timaaaay(if I got the spelling wrong and it meant something apologies),
I get where you are going with this.
A.)It's Christmas and You Can "Get Both"
All of the "core" or "abdominal muscles" are certainly active during reasonably heavy squats. There are people who trumpet compound movements over dedicated "ab" work for this reason. Many have good results. Others make "core work" a focus and they do well also. Finally, there are those who tend to do some ab/core work at the end of workouts or "a bit every day" because while it doesn't seem to help a ton, if it is neglected things do not run as well. I am in the last category.
It is worth noting that "ab" training is usually not terribly taxing so adding a few sets every day or at the end of a workout is not a difficult feat. It is not like trying to do a ton of squats, push presses, deadlifts, power cleans, and jumps in the same workout.
B.) Science and Shit
There are more players with trunk rotation and resisting rotation than merely the internal or external oblique. Intrinsic spinal muscles (very small and weak, so weak in fact that they may have more value in proprioception than imparting or resisting motion), the psoas muscles, contributions from the spinal erectors, etc. are all involved.
Another thing that should be noted is that there is very little rotation available in the lumbar spine. Like 2 degrees of rotation to each side (less between L5 and the sacrum)so we are talking like 9 degrees left or right of center total, a normal rotation to one side could fall between 6-18 degrees. Most of what we get for "trunk" rotation happens in the thoracic spine where rotation is much less limited.
Overall though, trunk rotation with a fixed or stationary pelvis is a pretty weak motion. On exercises that force it not a lot of weight is used. There is plenty of research to support a position that it is risky from an injury standpoint as well.
Now the ability to RESIST trunk rotation is very important and can be loaded. So exercises where the spine is held relatively neutral and torque is applied or the body as a whole pivots against resistance is a different ball game. The "Full Contact Twists" you mentioned in your other thread are an example of this. These are "body is one piece" exercises, credits to Dan John for the term.
The reason for the massive increase in loading is that the major player in "core" or "spine" stability is available if we are just trying to keep in the same position. That is intra-abdominal pressure and it comes from contracting the abdominal muscles in concert with the pelvic floor, diaphragm, small spinal muscles (possibly more for proprioception) and psoas in concert.
Within this frame having a "strong, stable" core has much less to do with having "strong abs" than it does with possessing "coordinated abs". Exercises that allow this coordination to take place/require it such as squats, deadlifts or gymnastic exercises like planks and dragon flags start to make sense.
C.) It's Christmas Eve and All Your Science Shit Makes the Baby Jesus Cry!!!
If we are talking about punching hard here what we really need to concern ourselves with is not pissing away the momentum that we generate by stepping, dropping, or pivoting. The contributions that small sheet like muscles like the internal oblique can add to rotation (how much of a running start is 10 odd degrees anyway) pale in comparison to their ability to "lock down" and let us "put our ass into it".
Spinal rotation is not the major source of power with a hook. Even shoulder motion is not. Let us look at a master doing his thing.
Now where the "resistance" happens on those punches is at impact. Note how when Joe's fist hits his hip and shoulder are in a fairly vertical line. He is not twisted around his center, instead his navel, the bottom of his sternum, and the top of his sternum are roughly vertical. He pivots and his body weight goes into the other guy. The "twisting" can happen on follow through or before impact, but when we hit we want to be stable.
And before someone jumps on me about saying shoulder motion is not a prime source of power in a punch let us think about it.
Yes, the shoulder moves. It has to. The fist has to get where we want it, but it is not shoulder joint motion (gleno-humeral joint motion) that is the big deal. It is the motion of the body attached to the arm/shoulder. If this were not the case "arm puncher" would be a compliment. Want proof? Sit in a chair and hit a heavy bag.
PS: Bourbon is the proper choice for Eggnog. Also, bourbon is the proper choice if you do not have eggnog.