ISO?
In reality the rich get richer etc. etc.
Or they could take an 83(b) election when granted the options. Or they could exercise some fraction of their options. Or they could sell some of the shares in the multibillion-dollar secondary market when they exercise to pay for the taxes.
Your broader point stands. But there are more choices than “eat it.”
Effectively you can't unless the startup allows for it. I have stock and when I tried to sell on the secondary market exchanges all said that there's a lot of interest but due to the company always exercising right of first refusal no one will bother.
Most companies don’t require Board approval for transfers. (There are better ways to moderate the process.) Companies that do are the ones choosing to restrict their employees, not the tax code.
But since you ask, the stated purpose of AMT is to make sure high earning individuals are not using tax loopholes to avoid paying any taxes. I assume it applies to ISOs to prevent employees from being compensated only in ISOs to get the better tax treatment.
Having paid AMT myself on exercising ISOs, I concede its an annoying additional thing you have to consider when taking an offer from a startup. But its not some grave injustice. Tech employees at successful startups with in the money options will be just fine.