I think it will be made increasingly untenable to drive older cars, through legislation and increasing cost of fuel. There are already cities where you aren't allowed to enter with a vehicle that doesn't meet certain emissions standards, and this is likely to be rolled out more and more widely.With the current energy mix, EV cars cause about half the amount of CO2 emissions over their lifetime (including production) compared to ICE. So that's a 50% reduction. However, I worry that people are going to drive more because once they have invested in an expensive EV the cost of driving it is much less. I would definitely drive more if I had spent so much money on a car that enables cheap driving.
I really like EVs, but I will probably keep my (14 year old, little used) car alive for another 10 years because it makes more environmental and economic sense for me. 10 years from now, I think private ownership of cars will be less because for people who only use cars occasionally (like myself) it will make more economic sense to just use the cheap driverless electric taxis that I expect will be abundant by then.