I'm really failing to see the real impact. There have been hundreds of proofs, many of which are much more intuitive and do not involve trig, only geometric constructions and algebra (which they also use)
That wasn't the main thrust of the criticism. That point there was that I don't see how using more complex concepts (trig) to prove simpler ones (Pythagorean identity) gives you a whole lot of insight.
Which indicates that you're still missing the point. The Pythagorean Theorem doesn't need to be proven. It doesn't need another proof. The entire point is to use a method that hadn't been done before. There's no reason to use try to prove the theorem other than to attempt to do something people haven't been able to do. Math for math's sake.