For those where "nothing has ever happened when I do.....", my new old saying is "and nothing will happen...until it does"
A chain is only as strong as its weakest link. You're right though, many really heavy chains work fine if there's no tugging. But even then one runs the risk of that "weakest link" giving up. Plus, the weight one carries around with a chain. No thanks.
A strap is nick-named a "tugg'em strap" for a reason. Hook one up, leave about 1/3 slack, and take off running. The soft "hit" is almost undectable, and the actual pull is multiplied 3-5 times the weight value of your truck.
I have used them for about 30 years, and have pulled out much bigger trucks than my own in really sticky situations (mud, e.g.). I used a 2" in my Int'l Scout II, and the only time I ever got close to "breaking" one, was when it got sraped on the guy's bumper and it started to cut it. I made him buy me a new one. Lesson: use a softener on sharp edges. Plus, the strap is light and rolls up nicely in my side-arm box.
To each his own, but I personally will not ever use a chain. Just scares me too much. (that cut off cab made a believer out of me!)