This bill changes when taxes are due for non-quals.
You already pay taxes upon exercise of non-quals. So the ability to pay at exercise does almost nothing to further inequality. In fact it's hugely risky and in almost all cases, a bad idea that leads to lots of money lost. In that sense, having the money to pay the taxes (anyway) improves inequality to the degree that it saps the assets of those with family funds and distributes it (via programs paid for via taxes) to the less fortunate. The opposite of what you're claiming, and what is the case today.
This bill changes the tax to become due at vesting. It will either not pass, or will become immediately ineffective as vesting schedules change to a 10 year cliff, with a single [4-year] pro-rata vest upon termination. IOW, for tax purposes you won't vest-as-you-go anymore. You'll vest all at once upon termination. If you choose to not buy your options the company will cancel the option agreement. If you do choose to buy them, the tax consequences are identical as today. Such a thing would be awful for ISOs but for non-quals it doesn't matter. For ISOs you want to buy them early as you can. For non-quals you pay tax upon exercise, so you don't want to buy them as-you-vest anyway.
It's very poorly thought out.
This would have people paying taxes on fictional or purported wealth. As dumb as the tax code is, this isn't even reform.