I need to rephrase that for my own benefit, because I don't see how those pieces (bonds purchased while working; annuity at retirement; asset 100% depletion point) fit together.
As for "additional cost to the system," who gives a rip if its object is wealth transfer, ala "those that die early help pay for those that live to a ripe old age." Transfer money until Atlas shrugs.
It is obvious that if a modified system leaves wealth in the hands of the citizen, where now it leaves ZERO, the difference has to come from somewhere. Most of us see that "somewhere" as our own pocketbook. And the all-government-bond solution would leave the money in the hands of the government until the buyer retires (at which time the cash flow reverses - possibly under control of the government) or dies (at which time residual value transfers to heirs), only giving the buyer an "identifiable account," and disposing of the "private market is unreliable" argument because the account isn't subject to the whims of the stock market.
A series of government bonds, purchased at a rate of 12% of income, for a work period of 40 years (age 25-65), would produce a future income stream: 12% of 40K a year for 40 years, with 2% monthly compound interest, nets $294 grand - at 3% nets 370 grand - and at 4% nets 473 grand. I haven't checked the SS tables to see how the payouts compare (between SS and interest alone on accumulated principle), but even the best scenario would provide only 19 grand a year of interest only. I assume this is where your annuity would convert some of the principle into a series of payments.
If the system is really nothing more than old-age welfare, then let's start calling it that, and dispense with the pretense. Available to those who need it, unavailable if you are above poverty, and the tax system finances the payout.