Here is my understanding:
1. The DPI number embedded in a photo isn't meaningful. The only number that matters is the total pixels. If you print a 2000px image 10 inches wide you get a different DPI than it you print it 40 inches wide, no matter whether you specify 72 or 300 DPI in the image.
Same holds for displays. You'll never know what DPI your images are displayed at no matter if you specify it in the image or not. An iPhone will typically display an image at 2x the dpi (~450) from a MacBook Pro (~225) because the laptop has similar D (dots) but more I (inches).
2. As for 1920px, that may be enough for 90+% of people, but I can say for sure from my experience at SmugMug, the bigger display sizes are very popular among people with sharp young eyes and high density displays like 4K.
When SmugMug bought Flickr, they made a big deal about how they would roll out something like 5K image display sizes, and I noticed there was a lot of positive chatter among geeks on Reddit about that. Some photographers want to limit their display sizes tho, which is understandable.
3. The ideas behind Imgix are optimization and adapting to the insane variety of device resolutions. By optimization, I mean the tradeoff between speed and things like compression. You might like a very uncompressed image in your starbucks, but someone hiking remotely on cellular wants something very different. Same as for YouTube videos. I don't know how Imgix handles that, maybe Kevin does, and whether a poor connection causes them to deliver a more compressed image.
What I do know is Imgix does not deliver the original, but always an optimized image for whatever display you have. Far as I know, there is no way to fetch the original you uploaded to Cake.