He was elected in the first place right after the Finnish civil war which was won by the right wing whites (and it was the civil war that had many feel a monarch would be good for unity). The Social Democrats were ousted for a while and only one social democrat remained in the parliament at the time. The people in favor of republic in the right wing parties on the other hand boikoted the vote so only 64 of the 200 members of the parliament voted.
Frederick Charles of Hasse declined 14.12.1918 and there was a new elections in Finland in March 1919 where the Social Democrats made a return and other supporters of republic did well also so it would not have been possible for another monarch to be elected.