Why do we care about shareholders?

“We have a financial system that is run by private shareholders, managed by private institutions, and we’d like to do our best to preserve that system,” Treasury Secretary Tim Geithner said.

Why? Maybe someone can explain this to me. Why does it make any sense for taxpayers to give billions (or more) to these banks and not own the banks? Why are profits privatized and losses nationalized? I'm not saying anything new. Krugman has repeated this refrain ad nauseum. But I'm not asking rhetorical questions. I genuinely don't get it. The government bought preferred stock so as not to dilute existing shareholders' stake. But why the hell are we jumping through hoops to protect these shareholders? Why?

If I invest in a company by buying stock, and that company goes broke, I lose my money. Nobody protects me. But if a bank goes broke — the precious shareholders! We can't let anything happen to them! Please, give our money to the same people who just blew up our economy and give us nothing in return. We don't need any control over these banks beyond the tisk-tisking power of politicians. Just don't hurt the shareholders!

These banks are broke. They would be distant memories were it not for government life support. So why aren't the shareholders who invested in these now-bankrupt banks already wiped out? If not for the bailout, there would be no banks to hold shares of. Someone please explain it to me. Seriously.