There's no question the iPhone could do with less top/bottom bezel.
Regarding side bezels specifically, though, why are people so against edge screens? Genuinely curious. The edge technology allows for screens to fit into a smaller body. It's how the S7 Edge gets away with a 5.5" screen in the form factor it's in. I mean, look at this:
Less difference, but even when compared to the OnePlus 3:
As someone who enjoys the benefits that a phablet can bring, but not necessarily the size or form factor of phablets, this edge technology allows the best of both worlds. You get the larger screen and larger battery in a more manageable and one-hand friendly size. The S7E is my first phablet, and anytime I get the chance to try another phablet then go back to my own phone, I'm reminded of how amazing the form factor is. And it's largely in part thanks to the edge panel.
Is the concern about false palm touches? Those happen rarely. Is the concern about false finger touches when handling the device, say in landscape when watching something fullscreen? Sure, at first it was awkward, but once you learn how to handle it properly, it's no problem (same can be said about palm touches, too, actually). There's nothing here so challenging that none of us can adapt.
Doesn't novel technology typically have learning curves? This is no different.
If you don't like it, you don't like it. That's all fair. But if you haven't genuinely tried it and lived with it and learn to use it, you're not really giving edge screen technology the proper chance. The gains are superb. I've always argued that the edge software features are actually the least exciting thing about the Edge; rather, it's more the physical form factor, the way the screen pops, and the way it feels more natural sliding things out from the edge panels (like Android's slide out menus). That's where the real gain of the edge technology.
Perhaps this is one of those things, yet again, where people won't fully appreciate it until Apple does it (hello 2017 iPhone?). Just like what happened when 5+ inch screens started becoming popular with the introduction of the phablet smartphone. The concerns were similar. The learning curve was similarly challenging. I also believe that as edge panels become more prominent, the software will also get better at recognizing false touches. Just as today, software has adapted to larger devices and include features that help phablet phones be more usable one-handed.