I have absolutely nothing against traditional Classics though I’m not sure how good a fit they are with typical US public high schools today. However I’m pretty skeptical that a few years of Latin—as opposed to Spanish, German, or French (which I also took) or something else entirely—is a uniquely good use of time.
However, what makes latin special is that spanish, german, french, english and many european languages have significant history with latin as a language and has been tremendously influenced by latin. And it's not just language. Much of science, literature, music, math, etc has strong latin roots.
If there is one language that offers the most bang for the buck, it's latin. It's something every kid should be taught in my opinion, especially in the west since latin influenced nearly every language and academic field.
esperanto is different because it is easier to learn, so instead of taking years to mastery, you are done in a few months, and teachers can focus on proper learning techniques without fearing that students get demotivated because it takes so long. then you can apply those techniques to the next languages and hopefully come out ahead