Xenia, I don't think many people disagree with your last statement.
Socialism isn't about redistribution of wealth to the conclusion that everyone is financially equal; That's Communism in my mind. It's about making sure we have a decent level of minimum standards. Drawing a line and making sure anyone who falls below it, is helped back up again.
Yes, it's about higher taxes for those who earn more. I'm all for a 50% band though in reality, those who earn,say, upwards of 100k only make up a small percentage of the workforce (around 5%, I think) so I'm unsure how much revenue this would raise.
I think Pragmatic Socialists, (I've decided that is how I shall describe myself from now on! ) believe that state intervention/ownership is warranted in areas were concerns over profit making need to be removed from daily provision. Health and education being the obvious but also the police and fire services.
Of course, the irony is that relience on state funds creates more budget constraints that are seen in the private sector.