You can "give" a lot less money to homeowners than the value lost in the securities, because they will want to keep making payments they can afford in order to stay in their houses.

They will? How many of the threatened homes are owner-occupied right now? How many people would take the money and run, particularly given the falling market? How does a lump sum payment help with future unaffordable payments, or are we arbitrarily re-writing the terms of everyone's mortgage while we're at it?

Now, why would I want to reward companies and executives that irresponsibly made huge amounts of bad transactions when they were supposed to be the ones who knew better, and put not only their companies but all the rest of us at risk?

Companies have no personality, no humanity, and no conscience. "Punishing" a company is a convenient fiction - it means nothing and all that happens is that the costs of the "punishment" move down the line to shareholders and customers. As for punishing individual responsible actors, I'm all for it, and I think crouchback's suggestion of a decimation for the senior management of the investment banking sector would be a lovely idea. But it's a complete aside to fixing the problem, and conflating the two things isn't helping your thinking.