Now, why this happens in a brand new phone like the Pixel is another matter...
I went from a Note 4 to a Note 5, and ended up dropping my Note 5 causing the screen/LCD to break and not turn on. It looks like it costs about $300-400 to replace everything after asking a couple of local places, because the parts for this are expensive/out of stock. You might want to see if it's the same thing for the Note 4.
At that price, I'd probably just want to buy a new one.. but as you said, there's not a lot of good smartphones out right now.
I'm using the Note 4 again for now, which is actually a refurb/replacement because the original one's screen died randomly one day (without dropping it this time.)
One thing that really bothers me about a lot of the new phones is the slippery glass backs. The Note 4 has a textured plastic back with quite a bit of grip to it. I tried a friend's Galaxy S6 and it nearly slid out of my hand!
I suppose a silicone case would fix that, but I like being able to use the Note 4 without a case and not have to worry that it will slip away.
And as an aside, I dropped my Note 4 recently and broke the glass. I was thinking about the possibility of getting a new phone. But after looking at this season's options I'm heavily leaning toward just replacing the glass. One reason is that no top-of-the-line smartphone seems to have a replaceable battery to avoid these problems.
More generally, this season's phones are also cheap-looking and cheap-feeling. The Pixel feels like a $200 phone at best, with its cheap aluminum shell, fragile-feeling uncomfortable buttons, and ugly plastic/glass/whatever square on the back. I've been losing faith in Samsung's build quality (I've had some issues with my Note 4 and my previous Samsung phone, and the news about the exploding Note really turned me off the company). Even the latest iphone looks uglier than usual (that glossy bezel really doesn't do it for me, looks like a free phone you get when you sign up for a phone plan).
2016 is a really really bad year for smartphones. None of these machines seem like they're really worth their price. The next great phone is probably going to be one that doesn't feel like corners were cut.