If it works for that society then I don’t see why not. I always wish that Haile Selassie had been able to transition into a constitutional monarchy. At that point, he didn’t need to be a full blown statesman anymore since he managed to get many Ethiopians educated for a life in a modern public sector industry.
At most, he was only needed for cultural continuity and symbolism. However, on the other hand the monarchy for many Ethiopians was a source of animosity and was one of the factors of the Eritrean war of independence (which again, was due not only to the Muslim population there not wanting a Christian king but also because Selassie dissolved the regional government in Eritrea instead of turning the model into a road to a constitutional monarchy) so I guess this bring me back full circle because again, this question is best answered by individual countries.
With that said, I voted for the third option