That is true, but
No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President.
If he's not eligible, he is not, and never was, President. He would be illegally occupying the office. Impeachment by the House and removal by the Senate is for Presidents, not usurpers illegally occupying the office in violation of the Constitution.
How would you remove him from office then?
He is the highest officer in the land. SCOTUS does not have a national police force. Remember when President Andrew Jackson directly disobeyed a ruling of the Supremes with veritable impunity. Obama would have to order his own Attorney General to have himself removed from office.
Or would Biden suddenly knock on Obama's door and and say, "sorry Barry, it's been fun but you should not be here." "Hugs to Michelle and the kids." "I'll see you next time I fly AF-1 into ChiTown."
It's just pipedreams.