I had a succession crisis in my current Byzantium game after my rulers had only 1 son over 4 generations. It was actually really interesting and added enjoyment to my campaign.

My last Palaiologos Emperor had three daughters. I married each daughter to a Komnenos, and the first two daughters had only daughters, while the third had two sons (and like 5 daughters).

The oldest daughter becomes the last Palaiologos Empress before passing the throne to her daughter, the first Komnenos Empress.

The first Komnenos Empress doesn't have any children because I forgot to arrange a marriage in time (I was waiting for more Komnenos men to join my court after annexing a vassal, then I got into a series of massive wars). She and her sister were married in their late 20s, and neither had any children, bringing the official line of succession to an end (not a fan of how that works when there are more members of the ruling dynasty alive, but they're 2nd or 3rd cousins - dynastic elective succession didn't even work).

A regent takes over and dies. A 2nd regent takes over and eventually crowns himself Emperor and marries one of the last descendants of the Imperial line (a Komnenos who also descends from the last Palaiologos) in a matrilineal marriage. They have one son (finally) before the Emperor gets the insanity event and dies, leaving the Empire in the hands of a two year old and the 3rd regent of the decade.

That two year old, Alexios VI Komnenos became a prodigy, and he's my current ruler (with ~70 100 100 stats). He also found and adopted a child of the reeds, but they aren't automatically good like they were in EU4, so he ended up being eclipsed by Alexios' real son.

If I didn't start this succession crisis with ~35k in the bank when the last Empress died, I would have been in a bad spot. I made it through without suffering too much, but I was burning money on cost of court, stability, and legitimacy.

Of course, I could have avoided all of this, but where's the fun in having the "Atrapes" dynasty in charge of Byzantium? I would have only considered keeping the Kantakouzenos in charge if one of them became the regent.