What was the purpose? I think as Washington said in related matters -- "To avoid foreign entanglements."
The "natural born" clause is there ONLY because Washington wanted it there. He was a great man.
It is something exactly like the Obama's Dad situation he wanted to avoid. Why? He did not want to have a US President who was a Prince or a son of similar potent family.
Obama, himself, is the marker of the kind of entanglement Washington (and John Jay) wanted to avoid. How is that? When Obama went back to Kenya and campaigned for his cousin!
You mean Washington wanted write anyone like Lord Stirling out of contention for President?