This is nonsense: "Under the principle of separation of powers, the Constitution specifically disallows legislative officials from also serving in the executive branch. For the Speaker or the President pro tempore to become President, they must resign their position, at which point they are no longer in the line of succession. This forms a constitutional paradox to some."
The Speaker on becoming President would no longer be Speaker. Were the President and Vice President to die, the Speaker of the House becomes President. That's the law, and that's what would happen.
Yeah, right. You may believe it but it won't happen without a court battle.