I disagree on your stability statement with AWD. Equip a vehicle a vehicle with the same tires and you will find cornering stability much better a decent AWD system like that equipped on Subaru, Audi and Acura SH-AWD. The Acura system was so good(designed to enhance handling on dry pavement) that testers on frozen lakes were able to disable the vehicle stability control and perform things such as easing off the throttle during a turn and the vehicle’s AWD straightened the car out. Other AWD luxury cars compared (BMW & MB) spun out of control. Basically, these top tier AWD’s shift power to the appropriate tire based on current conditions.
Many passive AWD systems(part-time as needed) are simple 2WD(typically FWD) that kick traction on to rear wheels when needed and too late for stability. Basically to get you out of the ditch as you say. Volvo, Ford, Mazda, Honda, Toyota use this system. It does have the benefit less fuel economy penalty however do not impress owners too much when stuck. I have witnessed a few of them in sloped snow/ice covered ski slope parking lots.
I have 20 years experience driving AWD(mainly Subaru) and one Audi and FWD vehicles in New England winters.
Stopping I totally concur on not improved with AWD.