Glass protectors will not adhere to the edges - that's just a fact we're going to have to live with. You can try putting one on, then clamping it (very gently) for a couple of days until the glue sets and see if that improves it any. (I've heard reports both ways - it does.it doesn't.)
If you use a plastic protector, you still get scratch resistance. (Which is all a glass protector gives you - one that's well glued on, when it breaks, takes the screen with it. And with carbide particles [which are harder than tempered glass] being the main danger, scratch resistance is all you need.)
Maybe one of these days, those curved edges, since they're not very well tempered, will cost too much in warranty repairs, and the manufacturers will go back to flat glass.
Break protection? We'll have to wait for transparent steel for that.