A few major issues here.
1: You're testing a used shoe. Unless every shoe had the same number of miles, was worn by the same person (stride is different for person to person) and the same surface was used for the test, you introduced a huge variable that can't be accounted for.
2: Let's look at shoe design. The Mizuno has a hard plastic plate in the middle to rear of the shoe. It's pretty much impossible to bend it here. The Brooks appears to be a stability shoe with medial support, thus denser foam. So it makes sense it would bend at the path of least resistance. Asics Gel (seriously, they still use overweight Gel?) Cumulus 15. There's a plastic plate in the midfoot. Again, path of least resistance would have it bend in the forefoot section Can't say much bout the Saucony. The Pegasus you chose is a neutral shoe with no firmer foam or plastic midfoot section.
3: The "So What?" issue. Nobody runs with a 90 degree flexation. Ironically, the world's fastest shoe (Based on Kipchoge's 2:00:25 rabbited marathon this spring), the Vaporfly has a full length carbon plate that doesn't allow for much, if any flexation (I couldn't get it to flex on my pair at all). Given the shoe has a similar plate used in pretty much every track spike on the market that has a main goal of becoming a springboard to harness the energy and launch the wearer back up upon the end of the stride. If that weren't the case, then track spikes would be super flexible instead.
4: Everyone is different. That 50% injury rate could be pretty much anything. Overtraining, ramping up workouts too fast, too many workouts, not enough recovery, too many miles on concrete, not enough time in the chill pool or working on preventative strengthening, etc. To say it's the brand of the shoes is pretty ignorant. If they were really so bad, then why are most of the US's (and much of the world's) top runners sponsored by and running in Nike's without injury? Yes, everybody has a different stride and will feel right in different shoes. Some are more picky than others. Personally as a midfoot supinator, I can run in pretty much anything without issue. I'll just buy whatever is on sale in my size. Other people are much more picky.
5. As far as Nike being a "designer" or "show" shoe... then why is the rest of the running industry playing catch-up to Nike and Adidas with their midsole technologies? Nike released their Lunarlon foam in the mid 2000's and has been improving on it since. Foam is significantly lighter and more responsive than any "Gel" cushioning. How many other manufacturers were just re-hashing the same basic shoes year after year with little to no innovation? How many were using Gel as of only a year or two ago (Or still do, Asics)
6. You screwed something up during your "test". Here's a photo of pair of brand new Pegasus that flexes just like all of your other shoes. Flexes in the same spot as my brand new New Balance 1080's and my current pair of Sauconys.