On the contrary, the best part about having so much wealthy maintained in stocks is that other forms of wealth holding with with more objective value aren't effected. You don't want people to hoard cash as a means of holding wealth. You don't want people buying up commodities to store their wealth. Having wealth concentrated into pieces of paper that do nothing useful is ideal, because it's not clogging up useful resources.
Correction: I don't want them to hoard wealth at all. All forms should be taxed in such a way that none can act as tax-avoidance receptacles. In particular, if properties aren't actually used, there should be mechanisms to reclaim them or compell their use after a certain amount of time. And commodities serving a public good shouldn't be for sale/should be highly regulated and not very profitable, if at all.
But this is sort of beside the point: the primary point of this tax isn't to compell them to sell. So long as that wealth is generating income for the treasury, they can keep them. It's only the obscenely ultra wealthy with zero actual money who are encouraged to relinquish. That wealth can stay in share form... in a wider range of hands.
That's not the argument we're having. Everyone agrees that person should be taxed. Most people agree that person should be taxed more than they currently are. What we're arguing about is when they should be taxed, whether they should be taxed as the value is accrued or when it is realized, being sold or traded.
But in the system as-is, that tax can be perpetually postponed, and could ultimately be a small fraction. There's a very material difference. Even the 'when' matters quite a lot: the treasury's income shouldn't be dependent on the whims of the ultra-rich deciding to sell.