Grab your carbine...
....and stand with it shouldered facing the target. Aim, and fire. Now, drop the carbine and draw your pistol. Do you really want to move your feet to get into what feels right?
We train to have the exact same foot position with carbine, shotgun, or pistol. There's no realistic way to hold your long arm in the isocoles stance.
The schools that I've been to that teach Iso stance maintain that the body armor faces the target. The ones that teach Weaver mantain that it delivers a slimmer profile to the target, reducing your chances of being hit. I like Weaver, as it gives me a multi-weapon platform for shooting. After a couple of transitions from carbine to pistol, Weaver made the most sense.