With a full-size V8 Blazer or Bronc, locked front and rear, bigger tires, and full frame chassis, you have a lot more weight, traction, power and hard mounting points than most of us do with smaller, lighter SUV's. I run a 2007 Nissan Pathfinder and a 2000 Jeep XJ, and these are fairly light vehicles with smaller V6 engines. I've been out in some bogs with the XJ and found I just don't have the traction (on sand or mud) or horsepower to finesse another similar class vehicle out of sticky mud. But with a snatch strap I can generate enough momentum to yank another vehicle loose of the "suck" without risking damage to the limited hard points available on these unit-body designs, and once the suction is broken I can usually pull the rest of the way out of the muck without another snatch.

I've done a fair bit of off-roading and a snatch strap recovery is considered a safe and routine exercise. I always throw a couple blankets, jackets or towels over the line to dampen it if it should break. But from what others have told me (and this has never happened to me), if a strap does break, even with a lot of tension on it, because of its weight and large surface area, it doesn't pose the injury/damage hazard of wire cable or chain.

Winches are good too, especially if you're all alone. But many a time I've seen them overheat and shut-down before the stuck vehicle was recovered, or just not work at all for unknown reasons, or the recovering vehicle drag itself towards the stuck one instead of the other way around. If I get serious about building-out my XJ I'll probably put on a winch, but it's a low priority for me.

As for distance towing in an emergency, again I'd go with a snatch strap. As you observed, it's inevitable that some slack will develop in the line. I once towed a water-locked Jeep YJ about 3 miles through the NJ Pine Barrens on sand roads to get to pavement and waiting flat-bed, so my buddy could avoid a $1,000+ off-road recovery. I know I would have done some damage if I had used a chain instead of the strap.