You can do this at a public company because the RSUs are liquid. They can be sold at market rate on the stock market, for cash, which is what's given to the government. The government doesn't want your illiquid startup shares.
That's the exact purpose of stock options. From the IRS's perspective, when you receive shares in a private company, that's still income, because those shares have a specific value (determined by 409a valuation), despite them being illiquid.
Why the need for an exercise price(you can always keep it at a nominal amount like 1 cent) and short windows of redemption once you leave then? From most terms of options I have seen or heard of they have been quite restrictive compared to how flexible RSUs are.
Every year startups get a 409a valuation from an audit firm that determines what their company and shares are worth. The IRS requires that stock options have an exercise price that is equal to or greater than the share price that comes out of the 409a valuation. These are laws, not decisions made by founders/investors.
If you grant stock options with an exercise price that is less than the fair market value (share price from 409a), then that's considered income by the IRS and employees owe tax immediately.
With ISOs, the 90 day exercise window is required by the IRS. With NSOs, it can be longer, like 7-10 years. 7-10 years is obviously way more employee friendly.
Yes, kind of - what you're thinking of is known as an 83b election. But you still owe tax in the year you are granted the stock, at the current fair market value. If your startup is pre-funding, that's fine, it will be 10s of dollars. If your startup is funded, it will be 10s of thousands to hundreds of thousands of dollars.