The President can be Speaker?
Neat, if so.
“The President can be Speaker?”
You said it keep him out of, but it does not prevent him from becoming President because he can resign the speakership at any time.
Not to mention, name the constitutional clause that says the Speaker of the House cannot be the President. The House can nominate anyone as their Speaker.
Article I, Section2: “The House of Representatives shall choose their speaker and other officers; “
Nothing in there that says, “...and it cannot be the President.”