This answer is speculative, but I'm posting it as an answer and not a comment in the hopes that it will generate some discussion.
Why go sideways at all? Because it makes it look and feel more like a flying machine than just a car in the air.
First of all, it's potentially more aerodynamic. Look at the LEGO set: the wheels don't just flatten, they actually fold under the vehicle. It's certainly better for flying dynamics to not have wheel wells exposed, and it probably also helps with steering and balance to prevent the wheels from rotating freely.
Second, we're used to seeing flying machines that have retracting wheels: commercial airplanes. This is such a standard feature that it is likely to reinforce, consciously or otherwise, the specific visual impression of something that flies. The DeLorean wheels don't fold away, but they do fold. I think having a flat bottom surface is likewise important for conveying the impression of "hovercraft" or "airplane," both of which have flat or flat-ish bottoms.
Third, something visual needs to happen when the car takes off. It can't "just" take off: it would look ungainly. Imagine if the DeLorean's wheels didn't somehow change. Having some kind of outward transformation occur makes the vehicle look like a flying machine. On the flipside, having the wheels simply fold sideways, rather than fold into a special receptacle, specifically could suggest that the vehicle was retrofitted, which in fact seems to be the case in all the examples brought up here.
So not only do we have visual reinforcement of
"this thing flies"
but we also have visual reinforcement of
"this thing used to just be a regular car, and it's been retrofitted to become a flying car. but the retrofit was efficient and smooth rather than awkward and haphazard."
This, of course, is all in addition to the apparent wheel-as-lift-generator function we see in the DeLorean, Chitty-Chitty-Bang-Bang, and the Strange Tales "air car" (as per the other answer).