Asking honestly, is "I don't have money because it's all tied up in illiquid assets" a valid excuse? That's a personal financial planning choice, is it not?

It's certainly not an excuse for failing to pay income tax. Also, using a wealth tax, tax liability could be much more reliably predicted years into the future.

They can pay in shares.

So, sooner or later we end up with all companies being owned by the government. That has been proven to end up badly (by Soviet Union and rest of the communist countries).

The government can sell the shares to the public. Or the taxed individuals can can sell shares to the public and pay the government with the money. My point is that the company's illiquid assets needn't be used to pay the tax; they can be used to back liquid assets that pay the tax.