Taxpayer Funds Making Failing or Irresponsible Banks Bigger?

I'm no financial expert, have never claimed to be, but logical thinking yields some decent answers. How is it wise to allow taxpayer money, which is said to be necessary to save banks too big to fail, to be used to further isolate the banking industry to fewer players? Isn't that putting all of ones eggs in a single basket and promoting what is causing a key problem? Instead, it would seem that the more logical solution would be the break up the biggest banks, like Goldman Sachs, into smaller institutions. When is it ever wise to play an entire nation's banking system in the hands of a few CEOs? They have a name for that, criminal enterprise.