In OTL the US has managed over 200 years without having to actually use the provisions for succession beyond a Vice President.
In some ways this is statistically surprising,.
There were several cases when it could have happened.
Madison (though he eventually lived to a ripe age) was not in good health. Both of his Vice Presidents dies in office.
I believe that Tyler was quite ill in 1844.
Booth had hoped that his friends would have murdered, amongst other people, Vice President Johnson.
Of course Johnson was one vote from conviction in the 1868 impeachment trial.
Chester Arthur became quite ill.
Cleveland's first Vice President died, he was later to very ill with cancer.
There may have been other instances