I'm not so sure this is true. If you look back at the 18 presidents of the 20th and 21st centuries, only 6 can reasonably be classified as being "born to" an elite: the two Roosevelts, Taft, Kennedy, and the two Bushes.
The 12 others came from middle class to poor backgrounds.
One problem, with your analysis. The ones who were not “born to it” were all INSTANTLY swarmed with those who were as advisors, veeps, etc.
A classic example is Reagan. He was saddled with a Bush. He was saddled with advisors born to it. Same with the others.
The point is that they wil tolerate an occasional populist departure, as long as they can surround him and direct his policy. Ike was an example of this,, war hero, very popular. The “born to it” crowd knew they werent in danger in the slightest.