Tuning is a very messy subject, though. For instance, I think you're not strictly correct in your third paragraph - pythagorean tuning does theoretically admit of modulating to a different (at least "nearby") scale, since it is based on repeatedly applying the 3:2 perfect fifth interval! The actual problem is that it has bad thirds - hence "tempering", where basically, some of the 3:2 intervals are adjusted to move some of the thirds closer to being in tune. (It's true that this possibility of modulation was not musically exploited until after other tunings became popular - but strictly speaking, it is "just intonation" that can really only work for a single scale.)

For a simple introduction, I thought it would be better to skip the subject of tunings altogether and just focus on the structural implications that one would "read" in an actual piece of sheet music.