It's been done before. Will be a "Cash for clunkers" type thing. No one will force you to get rid of your ICE car, but they might give you a $$$$ incentive for a new one if they can crush your old one. I can't see it happening for several years, but I'm pretty confident it's going to be one of the measures they will use to incentivise people. ICE cars being sold right now will likely partake in the scheme. 
Personally I don't think they'll have to push very hard. Once EV's are available at good prices and with many choices, the carging network matures, and people actually understand how they work I think people will naturally migrate to them. The only people who will continue to run ICE vehicles will be people who have a need with a genuine EV-ICE capability gap and can afford the cost premium to run an ICE vehicle. 
One sample from Aus but I'm sure it's happened multiple times. Plus many places around the world. 
New Cash-for-clunkers Pilot Scheme Announced For Victoria, Australia - Auto Recycling World