I really don't understand why good employees work in startups instead of going to an IPO-ed company. Most of the time in the current climate they are worse off.

Many companies allow you to exercise your options and file an 83b election with the IRS. This only really works well though for the earliest employees because valuations often go up so fast that the exercise prices becomes prohibitive a year or two in. Then later, if your price is low and the stock price is high, exercising becomes cost prohibitive on the tax side where you pay taxes on the difference (AMT) even though you can't sell the stock. It is complicated issue but at its core is the IRS IMHO.

Usually you are allowed to exercise the options as soon as they are vested.

Employers need to get an independent valuation prior to issuing options. If you're hiring employees at a later stage, your hands are tied.