Or maybe we could just teach people about money and how to build wealth? The system isn't a 'rigged' as many claim. There are contless stories of people who managed to get rich that started with nothing.
Instead of making everyone poor, why don't we try to make everyone rich? Democracy means everyone gets the same chance, not a guaranteed result. Socialism means everyone is given the same result, regardless of how hard they work or how they educate themselves about money. Destroying the motivation for society to improve itself is not a way to make it better.
And just giving people money doesn't work without education on how to keep it and grow it. Look at sports stars and how most of them go bankrupt.
Eliminating stocks would mean a collapse of the economy (and of course it is a massive redistribution of wealth, contrary to your statement that it is not). Public compannies use public markets to grow. Destroying financing for business would not only destory the economy, but it would remove one of the easiest ways that ANYONE can make money. You don't need $1 million or special skills to make money in the stock market. You just need a bit of education.
Your plan seems to punish rich and poor alike. Hard to get excited about that.