The thesis of Robert Reich's idea isn't that the US become socialistic like the scandinavian countries. Rather that our economic polices return to what they were in the 1950s.
As regards taxing the top earners much higher... I don't think this was mentioned in Reich's documentary directly as I don't think it was one of the economic polices he was talking about (I'd have to watch it again). But nonetheless, and as an aside, taxing people more who make an enormous amount of money (like 1000x as much), where is the problem with that? It's not like it is causing any hardship. Consider two situations:
Person A Makes $40,000. He's in what, the 15% tax bracket (after factoring in deductions).
Person B Makes $30,000,000. He's in the 39.6% Tax bracket (assuming this is income, if it isn't it's mostly capital gains at 15% (I believe this was 25% in the 1950s)
After standard deduction and person exemption Person A's AGI would be around $30,000. His effective tax rate around 13.5%
He is left with a tax burden of $4050. So he has $35,950 (well not really after state, local, payrolltaxes, but let's ignore those).
Person B Subtract the standard deduction and personal exemption (which is a gross simplifation because he will likely be able to write off a lot more in tax deductions by itemizing...) His tax burden is ($30,000,000 - 10,000) * 39.6% (just took the top rate as the effective rate will skew close to this): $11.9 Million. After taxes he still has $18.1 Million.
So what happens if person A actually made $30 Million in income (or let's say capital gains too if it was taxed just as high) and had to pay 80% in taxes? He'd have a tax burden of 24 Million true, but he still would have $2,000,000.
Now yes he paid most of what he earned in taxes, but please explain to me how he is not living very very very very well off on a "paltry" $2 million?
Person A, most of his income will go to expenses. Person B, a fraction of his income goes to expenses and stimulating the economy. Most of it he will end up locking away in savings. You can only buy so much house, car, clothes, food before you have enough.
I don't see why that would impose any hardship on the super wealthy.