So we already invade your privacy to appraise the former, and the later has to be be public because companies need to know who owns what shares and the trading platforms need to associate users to shares they own. Both can be used by government to provide ownership details.
You would also want to wealth tax companies for total global cash-on-hand assets they have as well. Those are also required to be public record already. That way private business executives cannot tax haven their own stuff under an LLC, and companies like Google / FB are punished for hoarding hundreds of billions in offshore accounts they have no intent to spend or bring back into the states.
Of course, this is all saying "government should do X" which is just for entertainment, pretty much. The US is in no condition to act in the will of the people at all right now anyway, so its all speculation - you would have to fix the broken democracy first.
Henry George proposed this in the 1800's [0]
I'm not familiar with this being a requirement for foreign, private companies. (Reading between the lines, I'd expect a marked increase in investments in foreign, private companies under such a taxation scheme.)
Those with capital / assets can leverage up, borrow more money, and then pay it back with lesser inflated dollars.
Also the IMF's stance on inflation and inequality is moving from hyperinflation to sustainable inflation leads to reduced inequality but there aren't advantages to moving to a lower inflation than that.
Buying property?
What about just printing money? Not ideal obviously, but there'd be no way to avoid the inflation "tax".