Simply let them pay the tax with shares. Problem solved!

Well one thing is, they'd sell shares to pay the taxes. Then dilute their own ownership of the thing (Tesla, Amazon) and it would serve as another form of wealth distribution.

Charitably speaking: I suspect the commenter above you was indicating that the government should have a stock portfolio you can transfer stocks to to pay taxes in a non-taxable event type scenerio.

If you're taxing wealth (and not income) then switching stocks into cash doesn't change the wealth. Then use the cash to pay the taxes which reduces the wealth.

I believe the argument was that for some people, switching stocks into cash actually do change the wealth, because they own such a large % they are meaningfully moving the market by selling (the "paper money" argument).

And the answer to that was "if you're so afraid that selling will tank the value of the stock, then we [the government] will happily take your taxes as stocks directly, and we take on the risk that selling it will reduce its value".

which is also part of the idea of wealth taxes? to diffuse wealth?

Yes.