Hm.
I get the symbolism, and the symbolism is important. It would demonstrate that, whatever the demographics and the history, both communities are equal in the State.
It would work brilliantly if the presidency in Cyprus were a ceremonial head of state position, a symbolic Father/Mother of the Nation gig. The problem is that the presidency in the current Cypriot state is not ceremonial.
The 1960 constitution was pretty close to this power-sharing arrangement, by giving the Turkish Vice-President veto powers. Greek Cypriots complained that this was unworkable, and wanted it changed—which ultimately led to the 1963 intercommunal violence.
I don’t know the details; I don’t want to know the details, and I sure don’t want to get into a debate about them. But if the veto powers of the Vice-Presidency could trigger 1963, then turn-taking of presidential power could end up doing the same, lamentably.
You would want a lot more to be settled around checks and balances, a culture of political parties with bicommunal engagement, and a hell of a lot more Cypriotism (Cyprus First), for that system to be workable. (Or, just make the presidency ceremonial—but you’ve still got to fix the other issues anyway.)