In my career as a teacher I looked out for historical games to use in my history classes, but was usually disappointed.
For example, a game of the Spanish Armada in a popular partwork, aimed at children interested in history, which was simple to learn and play, so my pupils enjoyed it, allowed the English warships to destroy Spanish ships by gunfire. I then had to spend class time explaining why this was not the case.
Another game, this time on the English Civil War, that appeared in a textbook by a reputable publisher, was again easy to learn and play. But from its rules one would deduce the following:
No towns declared for Parliament at the start of the war. A Royalist force could never succeed in relieving a town loyal to the King if besieged by Parliament.
The Royalist army could never beat a Parliamentary army in battle in open country, but would always suffer a catastrophic defeat.
A Royalist army could never besiege and take a Parliamentary town or fortress, whereas Parliamentary armies always capture places they besiege.
The Royalist player can 'win', but only by being very careful to evade the Parliamentary army; not by fighting battles (which he cannot win) nor by besieging towns (which he cannot take).
so I declined to use it in class at all. Instead I devised a very simple set of ECW tactical rules, where guns needed to throw 6 to hit, made each child the commander of a regiment of Foot or Horse, and gave them a 'menu' of commands from which to choose each turn. At least they got some idea of just how unwieldy the units and armies were; in one game a commander of Horse muddled up left from right and charged off the battlefield; and the commander of a regiment of Foot in the second line opened fire on friendly troops ahead of him!
(For my own amusement, I an now rewriting the textbook game, trying to keep the simplicity but generate more realistic outcomes.)
Most, if not all, hobby wargame rules will be more realistic, but most of them are not specifically designed to be played by children with little or no historical knowledge, and so are – IMHO – unsuitable for educational use, being too long, complex and time consuming to set up to hold a child's interest or be suitable for use in class.
Home schooling use of wargaming by an enthusiast like your correspondent may succeed, but success will probably owe a great deal more to his personal input than to the wargame rules themselves.