Currently equity appreciation is desirable for HNWIs because wealth isn't taxed, only income realized is. The more their wealth appreciates, the more viable it becomes as collateral they can borrow against, raising their borrowing capacity. CEOs, the board and the major shareholders fall under this group too.
Stock buybacks artificially inflate equity value - cash rich companies buyback their stock just to deploy that cash and prop up their equity value. CEOs love this easy trick because it increases their equity holdings' value, and also lets them hit quarterly share price targets which allows them to accrue more equity options. But at the end of the day, this money isn't benefiting the company, so it's just air.
With a wealth tax, the incentive to acquire increasing wealth dampens somewhat. You're only taxed once you cross a certain threshold usually, but once you cross it, the resulting tax hit can be quite sudden and severe. You hold equity but you have to hand over a significant amount of cash immediately, so you'd have to liquidate your holding, which is why a lot of HNWIs hate it.
In fact, it's why there are active strategies (usually involving philanthropy and blind trusts) in Switzerland (which has a global wealth tax) that allow to optimize your wealth just so you stay below the threshold. But at least, that wealth isn't being hoarded and is being actively deployed in other ways.