You can't (IMO) reasonably ask someone to pay a cash tax based on a notional value for a transaction that never happened as that notional value will not account for the inevitable execution slippage that will happen if the shares are actually sold later. Let the government eat that slippage.
I think the people should not ask, nor accept equity payment as taxation.
I also think that taxation should only be on income. Wealth tax doesn't work well, and only hurts those who would use that wealth to produce more wealth (to the detriment of all). Taxing consumption is the best, but that's a little regressive, so taxing income is the next best thing.
As a matter of historical fact, governments do sometimes take equity in something, in exchange for what's owed. Like with the financial crisis bailouts.
It's a normal thing among and between capitalists, but also when the government interacts with them. I'm unclear on what principle would forbid it, when you start from the assumption that it's normal, rather than unheard of.
If you let people pay taxes in assets then demand for dollars would drop, and that’s a big source of American soft power.