An important thing to remember here is that Witherspoon was living in a time when “common grace” was understood to have given ancient pagan Greek and Roman philosophers enough knowledge of God to know that the world has a Creator and to know some basic things about the “natural laws” of that Creator.
This was not a new viewpoint, but rather was in line with what had been fairly standard Christian doctrine since the later days of the Roman Empire, when Christians in government and academia wanted to find some way to make use of the centuries of pagan accomplishments in law, philosophy and science from the heyday of Rome.
It is at least arguably a legitimate exegesis of Romans 1-3.
I personally do not hold to that view. I hold a much more radical view of the extent of human depravity, and would argue that in societies such as modern America and Europe which are aggressively jackhammering out the remaining vestiges of their Christian foundations, having already destroyed all of what remained of the above-ground portion of the building, common sense isn't that common.
An unregenerate mind in a culture of aggressively anti-Christian unregenerate minds is unlikely to see Christian presuppositions as common sense.
Rationalist can never bring themselves to accept “faith” without proof. And man cannot prove directly Christianity.
Reason is a wonderful gift, but you cannot become a Christian in a manner other than faith. That requires accepting many things that “can be seen” in people and the world that cannot be proven with science.
I have known many scientist, engineers and technicians. The more intelligent understood that science failed at explaining the “big picture”.
A good physicist friend explained to me back in the early 1980’s the accepted equations left a big piece of matter unaccounted for. He told me then that he expected a revolution in the reasoning of that science in the future.