Good topic. My 2.
I agree stale money or stale time both takes you into the negative.
But in all your situations mentioned, "emergency" means "immediately available". I don't think there's too many options besides Guaranteed Interest Savings Account that is both guaranteed slightly positive direction / and immediately available??? And another thought, I think there should be a cap somewhere for anything above the cap to get invested for better possible gain.
As for 401K, I'm a gambling man. I play my 401K like a roulette table. The 401k rep just laughs at me but I cashed out 6-7 years ago before the crash after playing since the beginning of 401k existence and bought a small house with it to use as a rental. I just started back up into 401K again this year with 27.4% gain for my first quarter with 100% invested in extreme high risk stock. I could loose it in an instant. And someone in the same program here may not loose as much as me. But I guarantee nobody here will make more either! 
I recall making 40%+ at times my first round into 401K.
But also to mention, I lost right at 35% of the cash out in penalties to NC and the Fed 6-7 years ago too. Taxes are ONLY going to go up. Probably take a bigger hit next time if I don't ride it out for the long haul.
