That would be wrong on another level entirely. Not sure it would have been a good idea for a king to be protected by a temple that's construction hadn't started until after the king's death.
Especially if it was a temple which that king had been specifically been told by God NOT to build.
The names Israel and Judah are used in the Bible with various meanings. Israel can refer to the specific person of Jacob. It also can refer to all 12 tribes descended from him. It also can refer to the country before it divided during the time of Rehoboam. It also can refer to the Northern Kingdom after the split.
Judah can refer to the specific person who was a son of Jacob. It can refer to the Tribe that descended from him. It also can refer to the Southern Kingdom after the split.
Redemption had to choose 1 definition for the "king of Israel" and "king of Judah" identifiers, and it made the most sense to go with the last definitions for both of those terms, since that is what applies to almost all the kings in the game. I understand that it is possible to find places in the Bible where the words are used differently, but the current ruling is consistent, clear, and concise. I think that's a pretty good thing