No thanks on an edge-to-edge display. I cringe thinking about accidental inputs while just holding the phone. The top and bottom bezels certainly need to be shrunk, especially the top (symmetry be damned), but the side bezels don't have much room to get smaller.
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And agreed with others in keeping the thickness status-quo and utilizing a larger battery. And how thin is too thin when it comes to structural rigidity? Back to the large top and bottom bezels, they likely aren't going to shrink much, if at all...so it's going to be a tall device, making damaging it easier if the thickness is decreased dramatically.