Even with the 83b, you'd still have to pay taxes on the current value. This is practical if the stock still has negligible value (i.e. you joined pre-funding), but otherwise you face being taxed on monopoly money.
My understanding is that you pay taxes not on the current value, but on the difference between the value of the stock and the price you paid for it. It's essentially treated as income.
That's correct. But if you're buying shares at non-negligible value then you're basically an investor at that point. No employee is going to do that.
More likely, the company might give away shares to an employee in lieu of salary, but then the employee has to pay taxes on the value.
In other words, there's no way to obtain stock in a private company without facing some kind of expense. You're either paying money directly for shares, or paying taxes on the gift of shares.
The only way to avoid any of this is:
1) Be there at the very beginning, when shares have negligible value and can be bought easily.
OR
2) Be granted stock options instead of real stock.
That's not how an 83b election works. Your grant price is the current value, so your taxable gain is 0 upon election. You only have to come up with the money for the stock. Also, you can make a partial election if you don't have enough to buy all of your stock. Many people mess this up.