On the delta value of longevity risk pooling

This is basically an update to a previous post on a paper on the utility of pooling (Notes on: Utility Value of Longevity Risk Pooling - Milevsky and Huang 2018). In that paper, which I considered to be useful and innovative, I had one point (ok, a lot of points) where I was particularly confused.  I couldn't completely get my head around one of the important innovations in the paper: his delta [δ0 = √ e − 1 ≈ 64.9%, when r = λ, γ → 1] (this would be in the absence of existing pension income and using exponentially distributed remaining lifetime which would change delta) which he describes as "the value of longevity risk pooling."

I figured this was pretty important so I couldn't let my confusion pass unmolested. And this is where I get to one of the things I like about retirement finance: when one is confused, all ya gotta do is ask, and 9 out of ten times, someone will respond in a helpful way.  So I asked.  To my (paraphrased here) email to Professor Milevsly asking "Can you explain what the heck 65% means and how I should interpret it?" the good professor responded: 

Hi Will. Basically, its DELTA percent of the money you have available to annuitize at retirement. So, if you have $100,000 and decide not to purchase the longevity insurance -- and take the chance of living longer than life expectancy -- you would need to be compensated with $100,000 times DELTA. moshe

Ok, so if his delta was an obscure or odd mathematical object before the email...then, after crossing the line called "ah, now I get it," it seems even odder.  I had been ruminating lately on the percentage of my capital that is "dead" because it is the portion I can't really tap because it self insures a superannuation risk that may never be realized. But this is something different. This is like some kind of shadow capital concept; it's as he says: the value of what I'd need to be paid not to annuitize wealth to cover the chances of living really long. It's like a parallel-universe-through-the-looking-glass version of my dead capital idea. If I have it right. Which always seems in question.  

Here is the page... Note the comment on the "actuarial economic interpretation to √ e" as if e were not already a cool enough number.  He goes on to a more general expression of delta for when mortality assumptions, pensionized wealth, and risk aversion are more realistic. In that case he uses a power function of two annuity factors where the denominator is a risk-aversion adjusted factor [ (a/a*)^x -1 ] but you can read that for yourself.