This thread is like watching a rugby player, a basketball Player, a football player, and a baseball player argue about changing the rules for field goals.
More seriously, I don't see much point in having a ceremonial head of state, nor much difference between the monarchic and republic variations on that theme. For practical purposes, the real head of state is whatever office in which the power of the state actually resides. Inventing nominal "head of state" roles just for the warm fuzzies you get from being able to say "technically the prime minister doesn't have ultimate authority" doesn't make any sense to me at all.
To me, arguing about which kind of ceremonial head of state to have misses the point entirely. Just get rid of the office altogether, and focus your attention on the people who are actually governing you.