Why would you exercise a stock option to receive stock you can't sell? If you can't sell it, it's not worth $1,000,000--it's a piece of paper that might one day be worth more or less than $1,000,000.
* When the company has an IPO, you only pay the Long Term Capital Gains tax rate (20%), instead of the standard income tax rate (39.6%).
* Once your stock options have vested, you have the freedom to leave at any time without worrying about taxes or losing your options.
So you can risk tens of thousands now to potentially save hundreds of thousands later, in addition to giving you some freedom.
It's very risky. The company might fail. The company might be successful, yet never have a liquidity event (acquisition or IPO). But you only join a startup if you believe it has a good chance at success. You're risking a huge amount of time and effort, so you may as well risk a bit of cash too.
1. Exercise your options, pay potentially huge taxes on it, and be left holding stock that is practically worthless because you can't sell it
OR
2. Give up your options and move on with your life
I know what I'd do.
(Hint: this is where part of the SV age discrimination comes from)