Secretary of State is #4, and that didn’t stop Madeline Albright from holding that position during the Clinton years. I believe the accepted solution is that the succession just skips over anyone who is ineligible.

I’m aware of that, I’m not aware that they’re required to be American born, it would be an interesting constitutional question if the president and VP died and the speaker of the house wasn’t American born.

Edit - looking into it further, I don’t see the same qualifications being required as president and vp. For example, one only has to be 25 and up to be speaker of the house, yet one has to be 35 for president or vp. So again, I wonder if they elected a 25 year old as speaker and then a plane crashed with the president and vp on board (not possible they don’t fly together but let’s play pretend) I wonder if the speaker would be promoted to president to maintain continuity of government or if they’d be passed over to whoever’s fourth in line that meets qualifications.