I suggest they would be combined.
To me, a "kingdom" refers to some sort of region that is ruled by monarchs, but the kingdom may be ruled by multiple different monarchies through the ages. Additionally, questions about "monarchy" can cover things such as changes to the monarch's power, the life of the monarch, etc. Those questions could also be framed from the viewpoint of the kingdom, but they would not necessarily be questions about the kingdom itself. I just don't think that kingdom --> monarchy == monarchy --> kingdom. It's not 1-1.
In my random ramble today, I looked at the same thing. While ihtkwot's answer makes sense, in the idea that while kingdom's are monarchies, monarchies are not necessarily kingdoms, looking at the set of questions that are presently tagged as "kingdom" (22) does actually follow the logic that a "kingdom" could be tagged as "kingdom" (so "Kingdom of Norway" is tagged "Kingdom" and "Norway" -- the "kingdom" doesn't help in understanding the context of the question at all). Hence, the majority follow the line of thought as expressed by the idea behind "monarchy" quite well. The ones which don't, looking through the topics, are:
- Topics where "kingdom" is used in the sense of an "independent principality", but which don't actually need a monarch (or a 'king' as the 'monarch' can be a 'prince', 'duke', 'archduke', etc...) -- 4, this, this, this, and this;
- Topics which are actual treatises on the "how" of a kingdom or governorate, which are more aptly questions on the setup of the political system (independent on the 'name' of the political system) -- 2, this and this.
Hence, I also side & support the "merge" of "kingdom" and "monarchy" as that is a broader umbrella for what is being discussed in the majority of the "kingdom" topics. The two which don't fit that criteria (though, in fact, I don't think "Genghis Khan ruled a kingdom"...) have other more suitable tags (I'd say these already exist on the questions as well, so none need to be added to those two).