In describing how it worked I think I may have been conflating half-remembered details from more than one company - and possibly also inserted a little "plausible reconstruction" of how I logically deduce these products do work, as opposed to how they describe themselves. Along those lines, although the products could be constructed as trusts in the way I describe, on second thoughts I doubt they actually are. I think (though I haven't checked) that the regulatory framework guarantees customers won't lose if an insurance company goes bust. In any case, that doesn't seem to be a risk that people here regard as worth worrying about. I suppose the important thing is that a scheme could be constructed in the way I describe, if any US company wanted to do it.
When I was trying to understand how this type of annuity could work, one thing I noticed after looking at mortality tables, is that if you make it to your late 80's/early 90's, there's a very long period when your life expectancy stays at about four years. Or to put it another way, for several years you have about a 25% probability of dieing each year, given that you've made it that far. That means that you should earn a fair return of 25% a year on your remaining capital in mortality bonuses alone. (This is in a hypothetical product that works as described indefinitely, I think the small print of the Prudential product switches you into something more conventional when you hit 90.) (Edit: actually that's a 33% return. Four customers with equal capital, one dies, the other three get a mortality bonus of one third.)
The other company who had a similar product was "Merchant Investors" however the last time I looked their product information was no longer available on the web. (The product was still available though.) I may have got the term "mortality bonuses" from them. They were the ones who, in addition to giving you access to managed funds, gave you an option of having a stock-broker account within your annuity. (For an extra annual charge, of course.)
A company called GE Life (I think they were Canadian-owned) used to offer a product that I think was structured along similar lines, but for drawing down home equity. In effect you would "buy" an annuity by transferring ownership of your home into the scheme, retaining the right to live there for life. In return you would get an income for life. The income could be linked to various funds, including a fund that owned all the homes transferred in. The homes would be revalued every three years, and as the value went up (or down) your annuity income would change accordingly. I thought this was a very innovative product, however I don't think it's available any more. (One unnecessary weakness in this scheme was that if you moved out of your home, maybe because you needed a care in an institution, you didn't get any compensation for vacating your home early. You could move home while within the scheme though. I can't remember the details of how differences in value between the new and original homes were accomodated.)
(For anyone dropping in on the middle of this thread who hasn't realised this yet, these are all companies and products in the UK. I mention them because the products are very interesting and I don't see any reason why US companies shouldn't start offering something similar.)