Not only this, but the offices of the SECDEF and secretaries of each service branch are also led by civilians, to which the JCS report. There are strict limits to the number of positions in those offices that can be filled by uniformed officers.
It's just that I think people forget that the office of the President, while important, is a civilian executive position. It is unlike Chief Justice, or a 3* General, which require lifetime commitments to achieve.
I believe it was intentional that the office of the President to be public and administrative, more like that of a mayor than of a king.
But being President of the US makes one the Commander in Chief. That's the highest military position we have in this country.