They tried this, several times in fact. Each time they lost their shirts.
In almost every case, people losing their shirts was a result of:
1). No real financial education
2). Concentration of assets in a limited set of equities
3). Impatience
Equity markets are volatile. Everyone suffers the same rise and fall of financial fortunes in the United States if everyone owns a "piece of the pie". If you want the people to (in the Marxist fashion) "own the means of production", then the people get to suffer when the "means of production" loses value. Nothing's ever going to be perfect. Many "lose their shirts" when they foolishly sell assets in a down market instead of just holding on to them. Others were suckered into concentrating stock in their own company into a 401(k) instead of using a diverse allocation of assets from other financial sectors (especially hedge assets, like gold). Still others foolishly invested in, as you said, Ponzis or other schemes.
When you're given the responsibility of owning the most-precious assets of society, bad people will show up and try to cheat you. Human beings can be horrible. New laws and regulations will not stop people from being awful.
Today, you can honestly say that the wealthy do own the "means of production" - the majority of equity in private enterprise. 50% of American's don't even own stock in anything, and a smaller percentage have never made an informed choice about which equities they might wish to hold (they have an index fund in a 401(k) or similar). If we could transition away from concentration of equity ownership among the wealthy/ultra-wealthy to a healthier model where those who are now less-wealthy begin acquiring a greater share of corporate equity, do you agree that would be a good or a bad thing? Especially if we could teach them how not to be cheated by scammer?
By the by, if you'd examine some of the most-recent scammers (like Madoff) you'd find that the rich can be scammed as well. The responsibility of ownership brings with it perils. If you really want people to have a stake in the future, then you must accept that some of them will screw it up royally. Babysitting adults in perpetuity requires taking away their ability to effectively own/control anything.
Taxation of course. I dont see there is a way around it.
I do. Taxation hasn't done anything to upset the growing trend towards concentration of wealth. If anything, a progressive income-based tax system
encourages concentration of wealth, since the taxing authority gains a greater share of society's wealth as it is earned by those in the highest tax brackets. It is logical that the taxing authority would govern in a manner that ultimately favors the profitability of those who would pay the most in taxes. But let us not be side-tracked by tax theory, and instead examine other methods outside of taxation that could permit the "lower classes" an opportunity to regain ownership of society:
1). Re-establish Federal government authority over corporations
Corporations in the United States are ultimately creations of the goverrnment. No matter how much anyone says, "I'm a self-made man and I built my business from the ground up!", the truth is that any corporation outside the sole proprietership exists solely at the discretion of the government in any capacity that can be recognized by the courts. It's been that way since British colonial times. If the Feds say, "Amazon, your corporate structure is now illegal, and you must dissolve", then it is so. More-importantly, the Feds determines rules for how shares can be created and distributed, and when, and by whom. If there is a need to encourage the wealthy to begin selling off their shares in major corporations, then the Feds have all the tools they need to begin circulating ownership of society among less-well-heeled Americans. There's a lot of ground to cover under this sub-heading, so if we must expand upon that later then so be it. For now, brevity.
2). Encourage financial education
Do something simple, like piggy-back on the EIC program to give small bonuses to those who can complete some mail-order/online courses (free, of course) in financial education. What are stocks? Bonds? Annuities? How do they work? Why should you (or shouldn't you) own them? Remember, these are the tools the rich use to stay rich. Don't act like wealthy people are all ultra-intelligent, meritorious members of society either. It doesn't take an IQ of 140+ to be wealthy. I'm sure someone with a 95-100 could handle it. Many already do.
3). Rethink our tax model
Prior to World War I, the majority of tax revenue in the United States was generated by: tariffs. Anyone who is interested in "originalism" and "returning America to its roots" has to give tariffs another look. Tariffs tend to do the most damage to those who rely on moving assets into and out of the country with little impediment. They do the least damage to those who rely on doing business with someone else locally. Which segues into the next point.
4). Penalize expropriation of assets/IP
Part of the push towards concentration of wealth in the United States involved expropriation of entire businesses from the United States to other countries to drive higher profit margins. Assign harsh (and if necessary, recurring) financial penalties to those who transfer production methods and IP to other countries in order to establish production in those countries, especially if those countries have low wage scales compared to the United States. Track their movements carefully to punish triangulation.