More info: https://nssdc.gsfc.nasa.gov/planetary/lunar/apollo.html
https://en.wikipedia.org/wiki/Wernher_von_Braun#NASA_career
I assume to have those two directions as two camps in your company, fighting each other generates the most optimal result. If you fail, the cautious camp wins and carefull analysis and slow methodic itteration become stronger.
If you win, the move fast team takes over and pushes towards new exploration data and scaling up towards new problem areas.
Ironically, if von Braun had got what he wanted then, there may have been no Moon race and no Apollo program.
[1] Angle of Attack: Harrison Storms and the Race to the Moon, Mike Gray, ISBN 978-0393325133
"After the flight of Mercury-Redstone 2 in January 1961 experienced a string of problems, von Braun insisted on one more test before the Redstone could be deemed man-rated. His overly cautious nature brought about clashes with other people involved in the program, who argued that MR-2's technical issues were simple and had been resolved shortly after the flight. He overruled them, so a test mission involving a Redstone on a boilerplate capsule was flown successfully in March. Von Braun's stubbornness was blamed for the inability of the U.S. to launch a manned space mission before the Soviet Union, which ended up putting the first man in space the following month.[citation needed]"
In the case of MR-2, was the schedule to have an orbital flight before what turned out to be Gagarin's day of destiny? The response to Glenn's flight leaves little doubt that, in the popular view, it is orbital flight that counts as being 'in space', and the start of the Moon race might have hung on that perception.
So are you refuting that the missions were incremental? Because if you look at the mission outcomes, they certainly were..