That means on the date the contract was accepted/executed, the total current "value" was the monthly payment x 12 months x the number of years in the term. In our case, it was a value that was a multiple of our original premium so yes, our total estate gross net worth increased with our purchase (amazing, isn't it?) rather than decreased.
If you believe this, I don't see why SS is any different. I understand you place a significant emphasis on whether more money will be received are you pass away, but I don't think that makes the value of SS drop from your formula down to $0.
Also, for your estate taxes and other purposes, SS may not count as part of your net worth, but it seems to me it should count as far as your "real" net worth as far as it's "income generating capacity" goes.
Finally, your formula of 12*payment*<years> is not correct because it assumes $1 today has same value as $1 20 years from now (that's why people refer to NPV to discount for future $'s).
As far as your comment "since SPIA is much less secure than SS stream", I can't agree (of course).
You have to remember that based upon conditions of the contract your SPIA (or other annuity) income is protected under state law under limits depending on where you live.
These protections are worse that SS protections in a number of ways. (E.g. if one were to move coverages may no longer apply; or in case of inflation adjusted SPIAs, the return from the protection will not be very valuable - i.e. getting your principal back is not that useful if inflation is high and you lost your inflation protected stream; or what happens in case of massive failures where funds run out; etc.)