Every policy has spillover effects. And its important to think about them.

If taxes go up, savings/private investment goes down. That is not trickle down economics and there is nothing controversial about that statement.
In fact Saez and Zucman, two economists behind the scenes of this wealth tax plan, have to counter this obvious issue.

They say:
"A potential concern with wealth taxation is that by reducing large fortunes, it may reduce the capital stock in the economy—thus lowering the productivity of U.S. workers and their wages.
However, these effects are likely to be minimal in the case of a
progressive wealth tax for two reasons. First, the United States is an open economy and a large fraction of U.S. saving is invested abroad while a large fraction of U.S. domestic investment is financed by foreign saving. Therefore, a reduction in U.S. savings does not necessarily translate into a large reduction in the capital stock used in the United States."


Regarding innovation: if the payoffs to risky innovation decline because the gains will be taxed more, then there is less incentive to take that risk. Again, not trickle down and not controversial.
And again, it is so obvious that Saez and Zucman have to address it.

http://gabriel-zucman.eu/files/saez-zucman-wealthtaxobjections.pdf