We've all seen winged formula cars overtake, so that statement is patently untrue.
Anyway, there are perceptions in place as far as what is considered "modern" and/or "up-to-date" that effectively make F1 cars WITH wings a requirement. Also, at the speeds of current formula cars (F1 or other categories), having substantial downforce for the car's inherent stability is considered a necessity.
Besides, with current side impact and rollover protection requirements, you can't make a new F1 car without wings that will actually look right. The days of the Maserati 250F or the wingless Lotus 49 are long gone.
Anyway, as long as you have relatively basic wings, compared to what we have presently, the interference to overtaking is pretty minimal; it would certainly have far less impact than does all the blocking that goes on in the races anymore. You could make all the changes in the world to reduce the aero, but you won't notice a damn bit of difference in the races until you crack down heavily on drivers "driving a wide car". It's just that simple.
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