I think the sine/square wave analogy has some merit when comparing a non-elastic tether to an elastic tether - either a traditional tow strap, a chain, wire rope, etc. vs a snatch strap or recovery rope. In practice - polyester vs nylon. There's a big benefit to using the minimum necessary force and the elastic straps and ropes do that well. The analogy doesn't necessarily fit the comparison between a snatch strap and a recovery rope very well - because they do the same thing. When Matt's Offroad did a back to back comparison the strap was a softer pull. Just one sample event. But it's hard to make a comparison without some measurable data.
The biggest red flag for me is that same arguments for the rope are repeated nearly verbatim. The stitched loop part especially. Yes they are stitched. No, the stitching doesn't fail. That's such a stretch of an argument that it doesn't pass the basic smell test. Rigging straps, seat belts, limit straps, you name it - they all stitch the ends and they last the lifetime of the strap. It's a non-issue on any properly manufactured strap. The same is true about the claim that a snatch strap can only be used a few times. Does the elastic stretching break down the fiber? sure. Does it change them differently in a rope vs a strap? I don't think so. The only way this would make sense is if the rope is woven in such a way that each strand is stretched less as a percentage of its length - basically a 3 strand twisted rope or something similar (equivalent of using a longer rope or strap). The two arguments repeated suggest to me that it's not an original thought by the various sources - but rather a hallmark of a marketing campaign that couldn't find anything better. What I'm not seeing is any actual testing on testing equipment. And that equipment exists and I can find plenty of tests for straps and other ropes including snatch straps. If anyone has a link to an actual independent test, please post it. I'd love to see it. I'm open to being convinced. But not without some sort of evidence. Here's one for straps:
SNATCH STRAP COMPARISON - Unsealed 4X4 . Incidentally - some of the straps are as low as 10% elasticity and some as high as 25%. And only loosely correlated with cost.
The real benefit I can see is that they are more elastic if they actually are. 50% more as claimed is significant. If that is in fact true AND the elasticity is roughly linear in effective spring rate or at least more linear than the strap. If the first half of the stretch is under low tension - then it's not useful. But if we assume it's the same type of elasticity, but more of it - that's definitely a good thing. It gives you more room for error in the pulling vehicle to hit the end of the rope harder without damaging something and that means less attempts to pull to get to the minimum force necessary and less peak stress on the vehicles. Is it worth the extra space, weight, and cost? Possibly. It depends on how often you use it. I've had a strap hooked to my 4Runner once in 8 years. It's rare for me to find a situation where I wouldn't prefer to use a winch or have to use one. I also rarely see soft sand. I tend to think of that as the situation where it makes the most sense to use a strap. It's difficult to anchor against anything so using momentum is often the best option.
The lack of hard information is a problem either testing on product info. When I need rigging for my sailboat - I can call Samson Rope and they can tell me everything I ever wanted to know about a piece of rope, what testing was done, where it was made, what the fibers are, specific elastic elongation at measured tension for each rope product they offer. Every product they offer is tested and the results are available. I don't see any of those indicia of quality or testing from the recovery rope resellers (or the snatch straps). If any of the rope manufacturers wanted to prove their product was actually more elastic - it would be easy and relatively inexpensive to do at a testing lab. And many claim to be lab tested. Where are the test results? I'll email a few and see if they'll send them. Then we can compare with known test results.