The part of the question about perfect wheels and perfect surface (with as much friction as needed and no skid) is not that important. One can have an example in existing roadsways (albeit with good asphalt).
Now, friction is a force component which depends on velocity (or relative velocity between adjacent bodies or surfaces), moreover depends non-linear way. In the case of a car, the relative velocity is the velocity of the car itself.
One can do sample computations, but the intuition is based on the previous paragraph (which backs it up).
So, for a certain range of car velocities (small velocity), the car will actually turn, as expected, when the wheels do the instantaneous 90-degree turn.
As the car velocity grows larger, the car will not turn that smoothly, at some point it cannot turn because the non-linearity of the velocity-dependent friction will create such force components which will prevent the turn.
Also the part of car inertia (and car momentum) enters the picture and it is possible the car will do a complete u-turn (even in the opposite direction) or even turn upside-down.
Hope this answers the question.
The following was my answer for what happens without friction (misread the question too fast). However i wil leave it as it is still relevant to the whole answer.
Under these circumstances the car will not turn and also will not move (except if sliding due to another external force). Since both turning and moving the car (using the force transfered from the engine to the wheels) an amount of friction is needed. Isnt this sth, friction is needed for car movement :)
The mechanics of car movement is based intimately on friction between the surface of the "road" and the wheels. To move the car, the wheels (using friction) exert a force on the underlying surface (force generated from the car engine) and the surface, in its turn, exerts an opposite force which moves the car. Similar mechanics hold for turning the car, etc..
To have a vivid example, see a car trying to move on ice (sth similar happens also on sand, although seems counterfactual), the car will not move (except if it will slide by means of another force), since the wheels will have no friction (or minimum friction) to "hold on" to the underlying surface and thus receive the necessary opposite force which will move the car. Effectively the wheels push the underlying surface to one direction (and through an amount of friction) the underlyng surface pushes the car to the other direction, and thus movement (of the car).