I have a Prime, and I remember going through all the available apps ~6 months ago and uninstalling them all.
They were either bad apps in general or were potentially nice phone-sized apps with no optimisation done for tablets. When I say optimisation I'm referring to both the UI layout and the general rendering performance. For some reason (I'm not an android dev) certain apps have performance issues that scale with your pixel count (I guess they are hand-rendering things themselves and simply Doing It Wrong) and make them unusable.
I can't remember which though, so I'll install your top two when I get home (~8-10hrs) and report back.
Gah! So, I tried your top three and im sorry to report it's a trifecta of failure: Hacker News Beta renders really s
owly, Hacker News Android performs well but doesn't support landscape (it stays in profile) and Hacker News Droid performs Ok, rotates in landscape but without a useful or optimised layout, and as you state doesn't let you log in.