Earlier quoted context omitted.
I recall hearing about that for Zappos, but here the offer is repeated every year. Doesn't that ruin the effect - you know you can get (potentially even more) by quitting in a few months? And if it's only offered at certain times of the year, then there'll be a bunch of people hanging on until the offer comes around again.
Well, I suspect there will be people postponing quitting for a few months just so they can cash out with the offer. That's undesirable for Amazon. But I doubt you'd have people staying in a job they dislike for another year just to get an extra $1k when they do quit. Also you'll have compounded another year of turning down cash to work there so the cognitive dissonance might be even stronger.
The obvious solution to fix this flaw in the system would be to raise the offer daily instead of annually, be approximately $1000/365 =~ $2.74 per day. Or more simply by $20 per week, which comes out to about the same per year ($1040).