So buying up toxic assets is not incompatible with letting banks fail; if we pay market price, purchasing these assets may reveal a number of banks who are broke by removing unknowns from their balance sheet.
By switching to recapitalizing (euphemism for giving them money), we make no progress in removing unknowns from the balance sheet. This is why we're hearing about banks who are hoarding the capital instead of lending it -- they still don't know if they're broke or not.
Buying them up at market rate, as you say, would just make all the businesses fail. The whole problem is that the market value is almost certainly not an accurate indicator of the intrinsic value of these investments at the moment.
If the government made it clear that these businesses were on their own, then they would be forced to sell the assets at market rate, i.e. the amount the market is willing to pay for them.
If that's not enough, then as Anna implies, then they deserve to fail.
The problem is that if the banks don't like the market price, they don't have to sell. As long as they hold the assets, the credibility of their balance sheets may be in question, but why sell the assets for cheap and prove their own insolvency. As I understand it, this is the current gridlock.
http://blogs.wsj.com/marketbeat/2008/10/10/lehman-bonds-pric...