I agree that it doesn't feel cheap, it is actually surprisingly nice in my opinion. Is it a jewel like the One or iPhone? no. It is as nice as a Samsung. Yes.
As much as I would like to see Sony build the next nexus, I just don't see it happening. A "budget" minded product with limited branding opportunity just doesn't seem to fit with where Sony is headed. I don't see Sony building this phone at a price that allows it to be sold at $350.
What would be great however is the idea of multiple Nexus devices, with one of them throwing back to the old days of Google showcasing the ultimate potential of the platform. An elite version of the Nexus that has premium materials, and higher tier specs. Like this year we might have seen 4gb of ram, >3000mah, MEMS camera, hifi speakers, 4k screen. Off the charts specs. They might bundle it with a qi charger. They would not even try to make it affordable, it may even be limited production.
That is my dream!