They wouldn't, and the original poster isn't implying that they would.

I believe the argument here is that if the government wants to claim that these shares have a certain monetary value for tax purposes, then the government should stand behind that value and allow you to pay taxes with those shares at their claimed monetary value.

The end goal would be to prevent small business (or people with stock options) from going under because the government claims a piece of paper is worth $1m, but in reality it can't be sold at all, or couldn't be sold for such a high value. If the government claims "oh but we would lose 20% of the value in selling these shares" then they are essentially admitting that they overvalued them when taxing you.