Momentum is conserved, but not for just the car.
If you only think about the car you are not considering the whole system.
After all, you have two objects in the interacting system here. Wall and car.
It would be just as wrong to look at two snooker balls colliding where the cue ball stops and the other one moves away, and then point to the one ball and ask why its momentum was not conserved.
There is no law of physics that says 'momentum is conserved' for any object under all conditions.
The law states that for a system of interacting objects, with no external forces acting on it, the total momentum of the system is conserved.
The momentum of the individual objects does change. Of course it does.
Newton's 2nd law states it another way:
Rate of change of momentum is proportional to the applied force.
Yes: momentum changes in response to an applied (resultant) force.
So the car crashes into a wall.
The car is only part of the system of interacting objects. There is also the wall.
You cannot consider the car in isolation for conservation of momentum.
The total momentum of the car and wall taken together (the wall is connected to the ground and the whole planet!) is conserved.
From Newton's Law perspective, the car has been acted upon by an external force. It crashed into a wall.
So it's momentum has been changed by this force. This is what forces do to objects. It makes them move. It changes their momentum.
And if you think about it, and Newton's 3rd law, the car also applied an equal and opposite force on the wall, and changed the walls momentum. (By an equal and opposite amount.)
Ah you now ask....
'But the wall didn't move?' It's momentum was zero at the start and zero at the end.
Well, not quite.
The wall, connected to the earth and whole planet, has an enormous mass. So the change in its momentum, with such a large mass, meant that its motion was so small you could never observe it. But believe me - the car did transfer a little momentum to the planet.
Although, I suppose the car could knock the wall down and give some momentum to individual bricks. They would have observable motion.
You need to get out of the habit of thinking 'conservation of momentum' means that momentum (of an object) does not or cannot change.
The momentum of objects changes all the time in response to forces applied to them.
What doesn't change is the momentum of an object or a system of interacting objects that is not subject to any external resultant force.
I hope this helps.
Please ask again if you want further clarification.