In my experience most people at startups who leave end up not exercising their options due to the cost of exercising them coupled with the fact that they may be underpaid due to the assumption that their options may end up quite valuable. So basically they pay somebody 90k/year then give them ~20k/year in options. Then they quit after 2 years and have 90 days to buy like 50k worth of stock at the strike price they were promised.
So they end up paying 50k to buy some common shares (not preferred). An investor who paid 50k to invest in the company most likely got preferred shares, so the young guy who paid 50k who probably can barely afford that is now taking way more risk for a much smaller percentage of the company. If the company goes under the preferred shareholders have a chance to get their money back during a firesale of assets or IP or whatever, but the common shares are screwed.
So I tell virtually everybody unless there is a well established secondary market to sell your shares of your particular company, then don't take the options.
I honestly think the 90 day exercise is totally ludicrous in the startup world. I think that should be a major negotiation point with anybody who is joining a startup. They should just insist on it no matter what.
This is missing the key point of the article which is that there are also taxes to pay, not just the strike price. What you're saying is valid -- even the strike price can be a lot for someone to afford on their way out without any liquidity. But it is very important to understand that it's much worse than that at "successful" startups that have increased in value substantially over those 2 years. You also have to pay AMT (28%) on much of that gain in value, which could end up costing even more than the strike price itself.
Hopefully more startups will offer extended exercise windows of several years. Some are. See: https://github.com/holman/extended-exercise-windows