Yes, except I also studied the part where the US was intended to be an evolving nation where the laws kept up with change. I recommend you look into that part as well. Furthermore, you are really arguing for something that was very much an ideal, not a reality. The founders were politicians, through and through. They weren't interested in having their place in society removed by the average person. They didn't even grant the average person the right to vote. They ruled the nation, albeit through multiple factions, for decades after the Revolution, only ceding control when they were dead.
The older model, which as I said wasn't really reality anyway, slowly became impractical, especially for a technologically advanced nation. The adaptability of the American system is it's greatest strength. The rigidity you are arguing for is counterproductive, and really just impossible today. The idea that citizens with other jobs are going to have enough enough time and understanding to address an issue like nuclear waste disposal is asinine.
I don't care whether someone has ever ran anything before.
There is no such thing as being qualified to be president. It's too unique of a job. The President has more authority than he did previously because Congress constitutionally vested him with that power, due to necessity. It's not feasible for congress to do something like manage standing armies, or regulate nuclear power plants.
At some point, we have to deal with reality, not half baked a-historical narratives about the founders.