Sure the market for private, individual customers will still be there. But the vast majority of the "personal mobility units" - I don't prefer to call them cars because they won't be cars as we know them today - will be sold to the fleet , corporate customers: the "mobility providers".
IMHO owning your own "unit" won't be economical anymore. But people with strong desire for owning a unit, and those with enough money will still be able to own one. Or several units. Therefore strong car brands will survive. Owning eg. a Rolls-Royce or a Ferrari unit will provide a certain status, sure.
And in the transitional period a driver will be able to switch off the AD function in certain situations. While later on AD will be unswitchable and mandatory, and people will be able to drive the "units" (some brands will provide such feature) in the "controlled environment" . eg. racing tracks, driving polygons etc. I can even foresee "amusement parks" - a grid of famous roads & streets remade - where driving will be allowed under strict rules. Otherwise there will be VR driving simulators (games) available everywhere to everyone. Even using one - i.e. "driving" - while being driven in a mobility unit. Yes, today that sounds absurd but I can see that becoming a reality very soon.
And don't forget the flying (personal) mobility units ... Only sky's the limit!