Back in my years as a Catholic priest, I gave the idea of Apostolic succession considerable thought.

My problem was something new to our own era, something unthinkable in prior centuries, namely the possibility of a global thermonuclear war wiping out all living priests and bishops (it had to include priests because during a very brief period of church history the Catholic Church allowed priests to ordain priests).

The only solution I could come up with was that it would have to be possible for a priestless church to ordain both priests and bishops or else the church would cease to exist (at least the Catholic Church which is centered around the Eucharist, which, again, it believes only a priest or bishop can consecrate).

As far as I know, the Catholic Church has not formally considered this possibility to this day. Though it is less likely to happen now than, say twenty years ago, it is still a theoretical possibility, thus a theological problem they will need to address eventually.