Only you can say if it will spoil the sense of adventure. Also only you or your family can say whether that would work for you.
I will say that it will mean that you will need to know ahead of time where you will be each evening unless you stay in touch with the car via two way radio or something since I wouldn't depend on cell coverage. Also you will eliminate many of the hiker-biker sites since there is no car access to most of them. I would imagine that none of the hiker-biker sites allow you to arrive by car with the gear.
I always figured that having someone haul your gear is nice, but it complicates camping arrangements in some ways.
I don't know the family dynamics, so I hesitate to advise one way or the other. I will say that a car does simplify some things, but can complicate others.