Commercial banking needs competition now. What else would move banks to do what they are supposed to do - to lend?

Exactly! Businesses need to be able to finance their opperations now, exporters need letters of credit now, etc., etc.  The Fed and FDIC should be working together to identify and certify existing banks that have sound balance sheets.  It might help were the bank officers made personally responsible to the full extent of their personal assets, including trusts they have created, for the costs due to any bank asset that is not brought to the attention of examiners.  They, of course wouldn't likely be able to pay for the damage, but it would be a powerful deterrent to "forgetting" certain obligations.

Capital injected into sound banks would be lent to credit-worthy borrowers.  If these banks lacked experienced commercial banking officers, there should be many looking for positions about now.  Part of the FDIC's procedure for disposing of insolvent banks should be to see that the commercial lending operations of such banks are taken over by certified sound banks and that new capital proportionate to that department's size be injected into the recipient bank.  

Why couldn't government offer that banking competition, instead of distributing allowances?

The Federal Reserve Bank System is the only institution of which I am aware that could perform such functions, and their primary function is regulating the money supply, interest rates and banks.  They would be in an inherent conflict of interest and mission were they to take on large scale banking themselves.  Besides, they have been busy trading all of their treasury notes for toxic waste from AIG, etc.   and would be just another poisoned bank at this point.

Bruce McF has suggested upgrading credit unions to full service banks.  That should also work.  Why Paulson is not being called out for only taking obviously doomed actions is beyond my limited understanding if indeed there are explanations beyond my cynical expectations of his desiring to protect his cronies and his being blind to the needs of anyone outside of the world he came from.

As the Dutch said while fighting the Spanish: "It is not necessary to have hope in order to persevere."