The Mechanism of the Geithner Plan

I'm obviously missing something big here.

The Geither Plan creates public-private funds that can bid for securities presently held by banks. This pseudo-market will create a new "market price" for the securities, recapitalize banks (replacing the security they hold with cash), and restore private investor confidence in the securities (so that investors not participating in the funds or, like you and me, excluded from the opportunity will also start investing in the securities.)

Let's say a bank holds a security presently trading at $30, and lists the security on its books at $60. Let's say that the Geithner funds bid the price of that security up to $45, or even $50. Why would the bank sell it? The bank would have to take $10 loss on its books, and would end up being less solvent (on paper) than it was going into the scheme.

Paul Krugman estimates the value of the government's subsidy of these plans at 30%. If the "investors" are seeking to fully exploit that subsidy, and don't care too much about profit, they could in essence bid $60 on a security they actually believed to be worth barely more than $46.

Perhaps, then, Geithner's hoping that when objectively evaluated, the securities are worth between 10 and 25% less than their value on the books, so that bids will meet or even exceed book value while still leaving plenty of room for participating investors to profit. But that won't inspire others, not receiving the subsidy, to join in the "market", and as huge as this program is its success depends upon even larger amounts of private money to come into the market for these securities. And if the current market price is fair, the subsidy falls far short of what it will take to get the bids close to the banks' book value.

Also, if the new "market" results in banks being able to sell their securities for more than their book value, won't the magnitude of the subsidy become obvious? If Bill Gross believes that a security is not worth his money at $60, but is giddy to buy it through one of these plans for that amount or more, how does that establish anything but how stupid the plan is in the first place? (Or how clever, at least from Gross's perspective.)
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Update: Nouriel Roubini's answer to the question of whether banks will participate even if it means selling securities below book value? Mandate participation, and then deal with the consequence if a bank proves to be insolvent.