On public roads? No reason we'd have to license private cars for that, at least not for just any purpose.
Trying to ban all private cars while keeping our car-dependent civilization working is unrealistic, no matter how you look at it.
There's no quick fix at this point, it'd be a century-long project to undo the damage now, but a hypothetical world where we'd harnessed only the good parts of cars and not let them completely reshape the places we live down to the neighborhood level would sure be a lot nicer.
Less than a century ago, so within living memory (albeit only just), literally nowhere on Earth was car dependent.