Bailout: Banks or Mortgage Holders?

I know I'm not any sort of authority on failing banks and government bailouts but it still doesn't make any sense to me for the government to bail out the multitude of financial institutions that are failing miserably right now.

There's an article that I just came across on time.com entitled
Let Risk-Taking Financial Institutions Fail that seems to say what I hear a lot of other people saying.

However, I think the writers of the article are being WAY too gentle when they say: "Much of the crisis has arisen from miscalculating the risks involved in a large book of positions in these derivatives."

I think that it had more to do with influential people within the banks ignoring the risks because (for the moment) they were making money hand over fist (for themselves and the shareholders of the banks). I believe that organizations that have been taking huge risks (by loaning money to people who couldn't afford it along with many other risky things) should reap the consequences of their actions.

Why can't the government work out a plan that helps more of the people that are paying for it (the taxpayers that are losing their homes or watching them plummet in value) instead of corporations built on the whole concept of using greed as a business model?