The dangers involved in loosing a wing are when there is a load on it, driving down a straight you should be alright (maybe worse with the imbalance of two wings), but if a wing fails under load there is nothing the driver can do about it. Most small single seaters (be they F3, Formula Renault etc.) can race without wings. Look at Formula Ford 1800 add wings to them and it will completely change the car. In practice at Brands Hatch for a Formula 4 (club racing with a mixture of Zetec, CVH and bike engined single seaters running wings and slicks) a car crashed damaging the rear wing. The rear wing could not be repaired in time so both wings were sawn off to keep the car balanced and it raced without problems.
The reasoning against high wings would be on safety grounds, even with lenient 1960s safety standards they only lasted a year.