Obviously, Lotus was on the cutting edge of chassis/handling dynamics, but they were one of the few.
Cars were not necessarily designed to understeer in America until 1964 when the Corvair cases had put a real awareness out there. Prior to this, cars understeered due to a lack of desire to deal with the inherent weight distribution problems with big front-engined cars. Understeer was seen as safer, so why tune it out, no matter how much the car plowed?
In the 1960s, very few cars focused on handling -- trying to provide neutral-to-slight oversteer characteristics. Shelby did the best he could to improve the Mustang, while also working on making the Cobra controllable. (The 289 was the more successful racer due to the lighter weight/better balance.)
It wasn't really until the mid 1970s that American car companies focused on handling, and that was only due to Clean Air standards that robbed the cars of power. Corvette, Trans Am and a few other cars received more attention to futher handling abilities. This being said, the direction was to still maintain understeer characteristics.