Kings and Queens are the descendants of warriors and leaders of warriors who conquered the area. In a world with magic, warriors mean mages.
By the time you build up a large civilization, the combat capabilities of an individual pale before the coordinated combat capabilities of a trained military force. Technology and techniques will be developed for the use of magic in mass-warfare, and governments who arrange for effective use will dominate, and those who do not will be conquered.
At colonization of the americas equivalent stage, I'd expect the equivalent of Britian's empire would be fueled by mass magical education, where they crack the technique required for anyone to become a mage, and maybe ritual mass-combat magic, where even relative apprentices can be leveraged for mass magical effects, and industrial magic.
If a civilization figured that out, while others did not, it could experience something like the UK's industrial revolution (where a small island dominated the world). Others would start to copy it (but, mass education requires mass educators, and the social structure of a state where almost everyone has magic is going to be different from the typical magocracy) so this is going to take decades to catch up).
Meanwhile, at the top, the monarch is likely to have some magical education. But they need not be a top-tier combat or industrial mage: their power comes from the huge mass of the state, not from their individual magic. They are likely to have combat mage bodyguards, much like the monarch is going to have elite guards.
Rulers of monarchies in the age of steam where not expert engineers or top-notch warriors. They usually had some military experience and a good education, but that was to season them: their power did not flow from their personal prowess. The admirals and warriors and engineers served the crown, they did not rule it.
So I'd build the world where most of the world magical education is limited to the nobility, and are secrets passed down in families. The rising power has created a mass magical education system, where even peasants are taught narrow types of magic be more productive, and every soldier (often drafted from the peasants!) is a combat mage capable of helping in mass combat ritual magic and individual skirmishes. All backed by industrial-scale mass production of enchanted goods (even if they are just "modern" strength alloys).