No, it really doesn't. I think you're quite mistaken. Ultimately, most shares are held in funds which are pension or other personal wealth funds, and those are held by billions of ordinary people.
You've ignored the broader point about distribution. The Fed show that the top 1% own about half of corporate equities and mutual fund shares. So saying that shares are held by “billions of ordinary people” is quite wildly misleading.
My point wasn’t that ordinary workers own no shares through pensions or retirement accounts. But it is a limited and very unequally distributed channel for returning productivity gains to labor. It doesn’t make “shareholder profits” equivalent to “workers’ pensions.”
The key is that the wealth generated by workers makes its way into private pockets at many stages along the chain. Much of it never even makes its way to shareholders, neither through stock value increases nor dividends.
Yes, I agree, wealth inequality is massively skewed. But that is a different argument. In the end, if productivity increases and share prices go up, you and I are share holders (I presume you're saving for retirement), and we benefit. As does virtually every other person saving for retirement in the market.
Again, inequality is real, and is going to have to be addressed, but it is not the argument here.