Not odd at all. The throne of England has been occupied by Danes, Normans, Welsh, Scots, Dutch and Germans.
The natural born citizenship requirement for the Presidency was no doubt in part to prevent some foreign noble or prince from setting himself up as King of America.
I think it is one of Thomas Paine’s writings where he talks about a Frenchman from an old Norman aristocratic family who offered his services as king of America. He pointed out that his family was more distinguished that that of the English royal family since it had never had the taint of bastardy (William the Conqueror was known as William the Bastard before he conquered England). But if his services weren’t needed, he thought Congress should vote him some money for having offered to serve as king.