RSUs should be a lot more reality based, these are not options to purchase on a hypothetical future liquidity event, they're restricted stock that turns into real shares on public markets upon vesting.
Yeah kinda, you pay taxes on the market value of shares when they vest (become unrestricted). But only on the shares that have become unrestricted, not your still-restricted shares.
They are more common at public companies, but a company doesn't need to be publicly traded to give people RSUs. Conversely, a public company can pay in options rather than RSUs (or both) if they want.
Source: Work for a non publicly traded company and have RSUs not options, previously worked for a publicly-traded company that issued RSUs and options as part of comp