Re: If we taxed the rich properly
So basically the indolent wealthy prosper - while self-reliant workers are penalised.
Why do you think the rich are indolent? All the rich people I've ever known have worked their arses off, and even when stinking rich won't give up the habit of holding their own nose to the grindstone. Often this costs them any conventional definition of happiness, and frequently their personal relationships as well.
Your other points (which I think translates to one generally about marginal rates of tax) is valid, but what of it? "Fairer", ie higher taxes for the rich has been tried many times in many countries before - but the wealth of the very rich is usually globally mobile, and the evidence is clear that increasing the tax rate reduces the total tax take. Not to mention reducing the incentive to make yourself wealthy if penal tax rates reward the government more than they do the entrepreneur. Any sane person will move their money where it won't be exposed to excessive tax rates.
I might also add that being "rich" is about wealth ownership, not how much the individual accesses. So the Duke of Westminster might well be a bazillionaire, but if that's all in property or paper assets, all you can tax is his income - like you and I. You could try a wealth tax, but those too have a long and sorry history of not delivering the intended outcome.