Lithium-ion batteries use little or no RE, but the vehicle requires a light weight, compact, very powerful drive motor and generator plus motors to provide power steering, air conditioning, etc. All of these motors will require Rare earths. Rare earth demand will increase substantially.
Finding substitute is okay, it just the natural flow of technology anyway. My guess is every application running away from RE, there might be two, three or more new applications keen on using it knowing that supply won't be an issue in the near future. That will create a floor for RE prices and it just a matter of companies managing their profit margin. I'm certain that elevated (current) prices are here to stay and China will not be a cheap producer that it once was. A lot of medium/high paying jobs in China are now between $500-1000 or more per month so the income gap is not that large anymore.