I was taught the Weaver/Chapman at the outset, back in the 1960's, and I've never seen the need to change to the Isoceles, or its variants. One distinct advantage the Weaver offers, is that it naturally provides some protection of the user's center mass. The off hand arm provides protection to the torso.
The FBI Crouch used to have us place our closed fist in front of our hearts to deflect bullets too...we don't do that anymore either
The "natural" push/pull, or isometric grip helps provide balance. The slight offset of the feet also provide a stance in which the user is not so easily pushed off balance. Neither arm is fully extended, providing cushioning from recoil, and allowing recoil to come straight back, and not taking the arms upward, obscuring the target.
I would contend that enveloping the grip frame of a gun completely is more natural than an isometric grip. Have any child or untrained person hold a bat or stick, they just envelope it in their hands...they don't push/pull.
The recoil cannot come straight back, unless they bore line is below the center line of your hand, in-line with your forearm. Besides which your wrist, elbow and shoulder joints are working at off-set angles also...unless you are a Terminator. That displacement is what causes muzzle flip...it is also what allows us to call our shots
I've been to several self-defense classes where the isoceles was taught, but not one instructor has ever been able to establish any edge for the isoceles stance.
Just because someone teaches it, doesn't always mean they completely understand it's properties...especially if they wouldn't automatically point out the advantage of faster followup shots. Beside this the Modern Isosceles is:
1. More natural. The normal startle response is to square up with the threat
2. Working with the body. The body will always tend toward equilibrium, it will always try to unwind to equal tension on both sides. The late Paul Gomez has a very good video clip demonstrating this.
3. Faster to move from. Being a more balanced and fluid stance, you can move in any direction faster...that is one of the reasons the military uses it in movement training with the M4
They also teach techniques for closing the slide on a semi-auto, which runs counter to the design intents of the semi-auto. For instance, students are taught to grasp the slide with the off hand, pulling and releasing it to put the gun into battery. I was taught to use the slide release, keeping one's eyes on the target. By covering the slide, there is the possibility of riding it, increasing the chances of the weapon not going into battery. There's also the possibility of "missing" that is, not grasping firmly enough to disengage the slide lock, especially with a wet, or sweaty palm.
This would really be better discussed in another thread, however I'll address it briefly...
The reason it is taught is that it is more universal and is not dependent of the function of the platform to work. It works:
1. with an injured hand...you don't need a thumb present
2. regardless of the slide lock placement or presence
3. because you can't ride the slide down as the gun is driven out of the grasp of the support hand by the strong hand
4. when the slide has closed on an empty chamber.
5. because it is part of the universal stoppage drill and requires no additional muscle memory training
However, in the grand scheme of things, learn and practice what works for you.
This shouldn't be taken to imply that the Weaver has no place in modern shooting. Whenever shooting while moving laterally across targets, I'll use the Weaver