There aren't any wealth taxes of this nature on the books in the US, so assuming that they will only take cash and not shares is premature.
But I think you raise a good point that payment in shares is far more tenable, and likely probably, for highly illiquid economic assets.
This avoids all the problem incentive structure, and even worse tax code structure dealing with the fact that some years you make a return and in other years you make a loss.
Liquidity is solvable, if we're actually talking about a super wealthy tax with a floor of $50m and above. At that point, you are dealing with people individually.
In terms of "reducing the portion left which has to justify the risk/return proposition..." I don't think this applies. You have $1bn. You owe $10m in taxes. You owe that tax regardless of what you invest in, conservatively or otherwise.
It even solves some of that problem, if it replaces CGT. A CGT without loopholes (doesn't exist, and won't) disincentivizes risk. If you win big, you pay big. But of you lose, the IRS doesn't pay you. That incentivizes playing it safe.
IRL tax credits exist, and those more than compensate big CGT payers. In some famous example (eg Trump) derivative policies are big money generators. IE, invest for tax credit, not market gains.
But since this is really a "should" question (aka about values), theres not really a right answer. We can mostly just talk about fairness, of which there are many different conceptions.
My take: Society has to work hard to preserve the billionaire's wealth. You can't be king without an army, and billionaires exist because of laws, police and a social fabric that lets them keep owning so much stuff. You would otherwise have to be a warlord to keep your hands on so much, and that has its own costs and risks.
Perhaps we could look at it as a fee or compensation for the aggregate social guard labour required to preserve the social order that ensures the safety of the billionaire's assets.
Billionaires are still people. If they become too unsatisfied with their treatment, then they will do something about it. Just like everyone else.
Since I assume you're not literally suggesting that billionaires will arm themselves and I dunno, patrol their golf courses and beaches with rocket launchers, I suppose you are suggesting they buy some island and hire private forces, and I dunno, next they have to move their factories or offices there, and presumably hire workers and provide healthcare and education and retirement...
I guess if billionaire island seems like a really good deal, workers might move there. Without knowing more about (and assuming it doesn't just get annexed) it kinda sounds like Dubai.
Or sure they could try their luck in some other country if they feel safer there. Maybe somewhere that's happy to provide "inequality services" / free guard labour for them.
Re: billionaires taking over government so it works in their interests, this has basically already happened and these kinds of wealth tax proposals are a way to balance billionaires existing with the effort needed to sustain them.
And seriously when you look at the alternatives 0.5% (say) doesn't seem like such a bad deal.
Having startups that grow profitable, useful things at a healthy pace and that give back a small slice of their overall growth sounds like a pretty stable business model.
There's another problem which I'm surprised PG didn't address. Liquidity. A wealth tax means valuing property before it's even perhaps practical to sell it, and while the government might take your last 409a valuation as the means to valuing your net worth, they aren't accepting your shares as payment, only cold hard cash.
If you have a large private holding, now you are forced to find ways to throw off cash against that notional value, e.g. by arranging loans against your holdings to pay the tax man. Shares that ultimately never sell could end up being taxed for more then they are ever even worth.