Making generalizations

Hello..

In the following statement:

"A steering wheel is a rounded, bicycle tire-like handle that exists inside of every car and enables drivers to guide the movement of the car."

The above statement is meant to make a general definition, but here is a thing: it says a steering wheel exists inside of every car, though each car has its own steering wheel. So, to be precise, A steering wheel exists inside of a car, not every car, and we can then add that each car has its own steering wheel. I thought of how the indefinite article in front of a noun in such a sentence could be used to denote a whole class, but I still think there is a little bit of contradictory in that particular usage. I would feel much more comfortable understanding this sentences had it used the definite article instead:

"The steering wheel is a rounded, bicycle tire-like handle that exists inside of every car and enables drivers to guide the movement of the car."

In conclusion, this particular sentence is not itself the problem, but I meant to illustrate a usage form/pattern that's widely spread. Is it a common error? Or am I missing something here..?

I appreciate your help. Thanks.